| Title: | Geometric Data Analysis |
|---|---|
| Description: | Many tools for Geometric Data Analysis (Le Roux & Rouanet (2005) <doi:10.1007/1-4020-2236-0>), such as MCA variants (Specific Multiple Correspondence Analysis, Class Specific Analysis), many graphical and statistical aids to interpretation (structuring factors, concentration ellipses, inductive tests, bootstrap validation, etc.) and multiple-table analysis (Multiple Factor Analysis, between- and inter-class analysis, Principal Component Analysis and Correspondence Analysis with Instrumental Variables, etc.). |
| Authors: | Nicolas Robette [aut, cre] |
| Maintainer: | Nicolas Robette <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 2.2 |
| Built: | 2024-11-06 05:14:54 UTC |
| Source: | https://github.com/nicolas-robette/gdatools |
Draws various plots for Ascending Hierarchical Clustering results.
ahc.plots(ahc, distance = NULL, max.cl = 20, type = "dist")ahc.plots(ahc, distance = NULL, max.cl = 20, type = "dist")
ahc |
object of class |
distance |
A dissimilarity matrix or a |
max.cl |
Integer. Maximum number of clusters taken into account in the plots. |
type |
Character string. If "dist" (default), the distance between agregated clusters is plotted. If "inert", it is the percentage of explained inertia (pseudo-R2). If "loss", it is the relative loss of explained inertia (pseudo-R2). |
The three kinds of plots proposed with this function are aimed at guiding in the choice of the number of clusters.
Nicolas Robette
data(Taste) # clustering of a subsample of the data disjonctif <- dichotom(Taste[1:200, 1:11]) distance <- dist(disjonctif) cah <- stats::hclust(distance, method = "ward.D2") # distance between aggregated clusters ahc.plots(cah, max.cl = 15, type = "dist") # percentage of explained inertia ahc.plots(cah, distance = distance, max.cl = 15, type = "inert") # relative loss of explained inertia ahc.plots(cah, distance = distance, max.cl = 15, type = "loss")data(Taste) # clustering of a subsample of the data disjonctif <- dichotom(Taste[1:200, 1:11]) distance <- dist(disjonctif) cah <- stats::hclust(distance, method = "ward.D2") # distance between aggregated clusters ahc.plots(cah, max.cl = 15, type = "dist") # percentage of explained inertia ahc.plots(cah, distance = distance, max.cl = 15, type = "inert") # relative loss of explained inertia ahc.plots(cah, distance = distance, max.cl = 15, type = "loss")
Computes the cosines similarities and angles between the components of a CSA and those of a MCA.
angles.csa(rescsa, resmca)angles.csa(rescsa, resmca)
rescsa |
object of class |
resmca |
object of class |
A list of matrices:
cosines |
Cosine similarities |
angles |
Angles |
This function is adapted from csa.measures in sco.ca package.
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
## Performs a specific MCA and a CSA on the Music example data set ## and computes cosine similarities and angles data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") resmca <- speMCA(Music[,1:5], excl = junk) female <- Music$Gender=="Women" rescsa <- csMCA(Music[,1:5], subcloud = female, excl = junk) angles.csa(rescsa, resmca)## Performs a specific MCA and a CSA on the Music example data set ## and computes cosine similarities and angles data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") resmca <- speMCA(Music[,1:5], excl = junk) female <- Music$Gender=="Women" rescsa <- csMCA(Music[,1:5], subcloud = female, excl = junk) angles.csa(rescsa, resmca)
From MCA results, plots contributions to the axes.
barplot_contrib(resmca, dim = 1, which = "var", sort = FALSE, col = "tomato4", repel = FALSE)barplot_contrib(resmca, dim = 1, which = "var", sort = FALSE, col = "tomato4", repel = FALSE)
resmca |
object of class |
dim |
the dimension to use. Default is 1. |
which |
If |
sort |
logical. If |
col |
color of the bars |
repel |
logical. If |
The contributions are multiplied by the sign of the coordinates, so that the plot shows on which side of the axis they contribute, which makes the interpretation easier.
a ggplot2 object
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
# specific MCA on the Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # contributions of categories barplot_contrib(mca)# specific MCA on the Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # contributions of categories barplot_contrib(mca)
Between-class MCA, also called Barycentric Discriminant Analysis
bcMCA(data, class, excl = NULL, row.w = NULL, ncp = 5)bcMCA(data, class, excl = NULL, row.w = NULL, ncp = 5)
data |
data frame with only categorical variables, i.e. factors |
class |
factor specifying the class |
excl |
numeric vector indicating the indexes of the "junk" categories (default is NULL). See |
row.w |
numeric vector of row weights. If NULL (default), a vector of 1 for uniform row weights is used. |
ncp |
number of dimensions kept in the results (by default 5) |
Between-class MCA is sometimes also called Barycentric Discriminant Analysis or Discriminant Correspondence Analysis. It consists in three steps :
1. Transformation of data into an indicator matrix (i.e. disjunctive table)
2. Computation of the barycenter of the transformed data for each category of class
3. Correspondence Analysis of the set of barycenters
Between-class MCA can also be viewed as a special case of MCA with instrumental variables, with only one categorical instrumental variable.
An object of class CA from FactoMineR package, with the indicator matrix of data as supplementary rows, and an additional item :
ratio |
the between-class inertia percentage |
Nicolas Robette
Abdi H., 2007, "Discriminant Correspondence Analysis", In: Neil Salkind (Ed.), Encyclopedia of Measurement and Statistics, Thousand Oaks (CA): Sage.
Bry X., 1996, Analyses factorielles multiples, Economica.
Lebart L., Morineau A. et Warwick K., 1984, Multivariate Descriptive Statistical Analysis, John Wiley and sons, New-York.)
library(FactoMineR) data(tea) res <- bcMCA(tea[,1:18], tea$SPC) # categories of class plot(res, invisible = c("col", "row.sup")) # Variables in tea data plot(res, invisible = c("row", "row.sup")) # between-class inertia percentage res$ratiolibrary(FactoMineR) data(tea) res <- bcMCA(tea[,1:18], tea$SPC) # categories of class plot(res, invisible = c("col", "row.sup")) # Variables in tea data plot(res, invisible = c("row", "row.sup")) # between-class inertia percentage res$ratio
Between-class Principal Component Analysis
bcPCA(data, class, row.w = NULL, scale.unit = TRUE, ncp = 5)bcPCA(data, class, row.w = NULL, scale.unit = TRUE, ncp = 5)
data |
data frame with only numeric variables |
class |
factor specifying the class |
row.w |
numeric vector of row weights. If NULL (default), a vector of 1 for uniform row weights is used. |
scale.unit |
logical. If TRUE (default) then data are scaled to unit variance. |
ncp |
number of dimensions kept in the results (by default 5) |
Between-class Principal Component Analysis consists in two steps :
1. Computation of the barycenter of data rows for each category of class
2. Principal Component Analysis of the set of barycenters
It is a quite similar to Linear Discriminant Analysis, but the metric is different.
It can be seen as a special case of PCA with instrumental variables, with only one categorical instrumental variable.
An object of class PCA from FactoMineR package, with the original data as supplementary individuals, and an additional item :
ratio |
the between-class inertia percentage |
Nicolas Robette
Bry X., 1996, Analyses factorielles multiples, Economica.
Lebart L., Morineau A. et Warwick K., 1984, Multivariate Descriptive Statistical Analysis, John Wiley and sons, New-York.)
library(FactoMineR) data(decathlon) points <- cut(decathlon$Points, c(7300, 7800, 8000, 8120, 8900), c("Q1","Q2","Q3","Q4")) res <- bcPCA(decathlon[,1:10], points) # categories of class plot(res, choix = "ind", invisible = "ind.sup") # variables in decathlon data plot(res, choix = "var") # between-class inertia percentage res$ratiolibrary(FactoMineR) data(decathlon) points <- cut(decathlon$Points, c(7300, 7800, 8000, 8120, 8900), c("Q1","Q2","Q3","Q4")) res <- bcPCA(decathlon[,1:10], points) # categories of class plot(res, choix = "ind", invisible = "ind.sup") # variables in decathlon data plot(res, choix = "var") # between-class inertia percentage res$ratio
Bootstrap validation of MCA, through the computation of the coordinates of supplementary variables for bootstrap replications of the data.
bootvalid_supvars(resmca, vars = NULL, axes = c(1,2), K = 30)bootvalid_supvars(resmca, vars = NULL, axes = c(1,2), K = 30)
resmca |
object of class |
vars |
a data frame of categorical supplementary variables. All these variables should be factors. |
axes |
numeric vector of length 2, specifying the components (axes) to plot. Default is c(1,2). |
K |
integer. Number of bootstrap replications (default is 30). |
The bootstrap technique is used here as an internal and non-parametric validation procedure of the results of a multiple correspondence analysis. For supplementary variables, only "partial bootstrap" is possible. The partial bootstrap does not compute new MCAs: it projects bootstrap replications of the initial data as supplementary elements of the MCA (see references for more details).
A data frame with the following elements :
varcat |
Names of the active categories |
K |
Indexes of the bootstrap replications |
dim.x |
Bootstrap coordinates on the first selected axis |
dim.y |
Bootstrap coordinates on the second selected axis |
Nicolas Robette
Lebart L. (2006). "Validation Techniques in Multiple Correspondence Analysis". In M. Greenacre et J. Blasius (eds), Multiple Correspondence Analysis and related techniques, Chapman and Hall/CRC, p.179-196.
Lebart L. (2007). "Which bootstrap for principal axes methods?". In P. Brito et al. (eds), Selected Contributions in Data Analysis and Classification, Springer, p.581-588.
ggbootvalid_supvars, bootvalid_variables
data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") resmca <- speMCA(Taste[,1:11], excl = junk) supvars <- Taste[,c("Gender", "Age", "Educ")] bv <- bootvalid_supvars(resmca, supvars, K = 5) str(bv)data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") resmca <- speMCA(Taste[,1:11], excl = junk) supvars <- Taste[,c("Gender", "Age", "Educ")] bv <- bootvalid_supvars(resmca, supvars, K = 5) str(bv)
Bootstrap validation of MCA, through the computation of the coordinates of active variables for bootstrap replications of the data.
bootvalid_variables(resmca, axes = c(1,2), type = "partial", K = 30)bootvalid_variables(resmca, axes = c(1,2), type = "partial", K = 30)
resmca |
object of class |
axes |
numeric vector of length 2, specifying the components (axes) to plot. Default is c(1,2). |
type |
character string. Can be "partial", "total1", "total2" or "total3" (see details). Default is "partial". |
K |
integer. Number of bootstrap replications (default is 30). |
The bootstrap technique is used here as an internal and non-parametric validation procedure of the results of a multiple correspondence analysis. Following the work of Ludovic Lebart, several methods are proposed. The "total bootstrap" uses new MCAs computed from bootstrap replications of the initial data. In the type 1 total bootstrap (type = "total1"), the sign of the coordinates is corrected if necessary (the direction of the axes of an ACM being arbitrary). In type 2 (type = "total2"), the order of the axes and the sign of the coordinates are corrected if necessary. In type 3 (type = "total3"), a procrustean rotation is used to find the best superposition between the initial axes and the replicated axes.
The "partial bootstrap"" (type = "partial") does not compute new MCAs: it projects bootstrap replications of the initial data as supplementary elements of the MCA. It gives a more optimistic view of the stability of the results than the total bootstrap. It also runs faster. See references for more details, pros and cons of the various types, etc.
A data frame with the following elements :
varcat |
Names of the active categories |
K |
Indexes of the bootstrap replications |
dim.x |
Bootstrap coordinates on the first selected axis |
dim.y |
Bootstrap coordinates on the second selected axis |
Nicolas Robette
Lebart L. (2006). "Validation Techniques in Multiple Correspondence Analysis". In M. Greenacre et J. Blasius (eds), Multiple Correspondence Analysis and related techniques, Chapman and Hall/CRC, p.179-196.
Lebart L. (2007). "Which bootstrap for principal axes methods?". In P. Brito et al. (eds), Selected Contributions in Data Analysis and Classification, Springer, p.581-588.
ggbootvalid_variables, bootvalid_supvars
data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") resmca <- speMCA(Taste[,1:11], excl = junk) bv <- bootvalid_variables(resmca, type = "partial", K = 5) str(bv)data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") resmca <- speMCA(Taste[,1:11], excl = junk) bv <- bootvalid_variables(resmca, type = "partial", K = 5) str(bv)
Computes a Burt table from a data frame composed of categorical variables.
burt(data)burt(data)
data |
data frame with n rows (individuals) and p columns (categorical variables) |
A Burt table is a symmetric table that is used in correspondence analysis. It shows the frequencies for all combinations of categories of pairs of variables.
Returns a square matrix. Its dimension is equal to the total number of categories in the data frame.
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
## Burt table of variables in columns 1 to 5 ## in the Music example data set data(Music) burt(Music[,1:5])## Burt table of variables in columns 1 to 5 ## in the Music example data set data(Music) burt(Music[,1:5])
Coinertia analysis between two groups of categorical variables
coiMCA(Xa, Xb, excl.a = NULL, excl.b = NULL, row.w = NULL, ncp = 5)coiMCA(Xa, Xb, excl.a = NULL, excl.b = NULL, row.w = NULL, ncp = 5)
Xa |
data frame with the first group of categorical variables |
Xb |
data frame with the second group of categorical variables |
excl.a |
numeric vector indicating the indexes of the "junk" categories in |
excl.b |
numeric vector indicating the indexes of the "junk" categories in |
row.w |
numeric vector of row weights. If NULL (default), a vector of 1 for uniform row weights is used. |
ncp |
number of dimensions kept in the results (by default 5) |
Coinertia analysis aims at capturing the structure common to two groups of variables. With groups of numerical variables, it is equivalent to Tucker's inter-battery analysis.
With categorical data, it consists in the following steps :
1. Transformation of Xa and Xb into indicator matrices (i.e. disjunctive tables) Xad and Xbd
2. Computation of the covariance matrix t(Xad).Xbd
3. CA of the matrix
An object of class CA from FactoMineR package, with an additional item :
RV |
the RV coefficient between the two groups of variabels |
Nicolas Robette
Tucker, L.R.. (1958) An inter-battery method of factor analysis. Psychometrika, 23-2, 111-136.
Dolédec, S. and Chessel, D. (1994) Co-inertia analysis: an alternative method for studying species-environment relationships. Freshwater Biology, 31, 277–294.
data(Music) # music tastes Xa <- Music[,1:5] # gender and age Xb <- Music[,6:7] # coinertia analysis res <- coiMCA(Xa, Xb) plot(res) # RV coefficient res$RVdata(Music) # music tastes Xa <- Music[,1:5] # gender and age Xb <- Music[,6:7] # coinertia analysis res <- coiMCA(Xa, Xb) plot(res) # RV coefficient res$RV
Coinertia analysis between two groups of numerical variables
coiPCA(Xa, Xb, row.w = NULL, ncp = 5)coiPCA(Xa, Xb, row.w = NULL, ncp = 5)
Xa |
data frame with the first group of numerical variables |
Xb |
data frame with the second group of numerical variables |
row.w |
numeric vector of row weights. If NULL (default), a vector of 1 for uniform row weights is used. |
ncp |
number of dimensions kept in the results (by default 5) |
Coinertia analysis aims at capturing the structure common to two groups of variables. With groups of numerical variables, it is equivalent to Tucker's inter-battery analysis. It consists in the following steps : 1. Variables in Xa and Xb are centered and scaled 2. Computation of the covariance matrix t(Xa).Xb 3. PCA of the matrix
An object of class PCA from FactoMineR package, with an additional item :
RV |
the RV coefficient between the two groups of variabels |
Nicolas Robette
Tucker, L.R. (1958) An inter-battery method of factor analysis. Psychometrika, 23-2, 111-136.
Dolédec, S. and Chessel, D. (1994) Co-inertia analysis: an alternative method for studying species-environment relationships. Freshwater Biology, 31, 277–294.
library(FactoMineR) data(decathlon) # variables of results for each sport Xa <- decathlon[,1:10] # rank and points variables Xb <- decathlon[,11:12] # coinertia analysis res <- coiPCA(Xa, Xb) # plot of variables in Xa plot(res, choix = "ind") # plot of variables in Xb plot(res, choix = "var") # RV coefficient res$RVlibrary(FactoMineR) data(decathlon) # variables of results for each sport Xa <- decathlon[,1:10] # rank and points variables Xb <- decathlon[,11:12] # coinertia analysis res <- coiPCA(Xa, Xb) # plot of variables in Xa plot(res, choix = "ind") # plot of variables in Xb plot(res, choix = "var") # RV coefficient res$RV
Adds concentration ellipses or other kinds of inertia ellipses to the cloud of individuals of a MCA.
conc.ellipse(resmca, var, sel = 1:nlevels(var), axes = c(1, 2), kappa = 2, col = rainbow(length(sel)), pcol = rainbow(length(sel)), pcex = 0.2, lty = 1, lwd = 1, tcex = 1, text.lab = TRUE)conc.ellipse(resmca, var, sel = 1:nlevels(var), axes = c(1, 2), kappa = 2, col = rainbow(length(sel)), pcol = rainbow(length(sel)), pcex = 0.2, lty = 1, lwd = 1, tcex = 1, text.lab = TRUE)
resmca |
object of class |
var |
supplementary variable to plot |
sel |
numeric vector of indexes of the categories to plot (by default, ellipses are plotted for every categories) |
axes |
length 2 vector specifying the components to plot (default is c(1,2)) |
kappa |
numeric. The kappa value (i.e. "index") of the inertia ellipses. By default, kappa = 2, which means that concentration ellipses are plotted. |
col |
vector of colors for the ellipses of plotted categories (by default, rainbow palette is used) |
pcol |
vector of colors for the points at the center of ellipses of plotted categories (by default, rainbow palette is used) |
pcex |
numerical value giving the amount by which points at the center of ellipses should be magnified (default is 0.2) |
lty |
line type for ellipses (default is 1) |
lwd |
line width for the ellipses (default is 1) |
tcex |
numerical value giving the amount by which labels at the center of ellipses should be magnified (default is 0.2) |
text.lab |
whether the labels at the center of ellipses should be displayed (default is TRUE) |
If kappa=2, ellipses are called "concentration" ellipses and, for a normally shaped subcloud, contain 86.47 percents of the points of the subcloud. If kappa=1, ellipses are "indicator" ellipses and contain 39.35 percents of the points of the subcloud. If kappa=1.177, ellipses are "median" ellipses and contain 50 percents of the points of the subcloud.
This function has to be used after the cloud of individuals has been drawn.
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
plot.speMCA, plot.csMCA, plot.multiMCA, plot.stMCA
## Performs specific MCA (excluding 'NA' categories) of 'Taste' example data set, ## plots the cloud of categories ## and adds concentration ellipses for gender variable data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") mca <- speMCA(Taste[,1:11], excl = junk) plot(mca, type = "i") conc.ellipse(mca, Taste$Gender) ## Draws a blue concentration ellipse for men only plot(mca, type = "i") conc.ellipse(mca, Taste$Gender, sel = 1, col = "blue")## Performs specific MCA (excluding 'NA' categories) of 'Taste' example data set, ## plots the cloud of categories ## and adds concentration ellipses for gender variable data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") mca <- speMCA(Taste[,1:11], excl = junk) plot(mca, type = "i") conc.ellipse(mca, Taste$Gender) ## Draws a blue concentration ellipse for men only plot(mca, type = "i") conc.ellipse(mca, Taste$Gender, sel = 1, col = "blue")
From MCA results, computes contributions of categories and variables to the axes and the overall cloud.
contrib(resmca)contrib(resmca)
resmca |
object of class |
The contribution of a point to an axis depends both on the distance from the point to the origin point along the axis and on the weight of the point. The contributions of points to axes are the main aid to interpretation (see Le Roux and Rouanet, 2004 and 2010).
A list of data frames:
ctr |
Data frame with the contributions of categories to axes |
var.ctr |
Data frame with the contributions of variables to axes |
ctr.cloud |
Data frame with the contributions of categories to the overall cloud |
vctr.cloud |
Data frame with the contributions of variables to the overall cloud |
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
# specific MCA on the Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # contributions of variables contrib(mca)# specific MCA on the Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # contributions of variables contrib(mca)
Performs a "class specific"" Multiple Correspondence Analysis, i.e. a variant of MCA consisting in analyzing a subcloud of individuals.
csMCA(data, subcloud = rep(TRUE, times = nrow(data)), excl = NULL, ncp = 5, row.w = rep(1, times = nrow(data)))csMCA(data, subcloud = rep(TRUE, times = nrow(data)), excl = NULL, ncp = 5, row.w = rep(1, times = nrow(data)))
data |
data frame with n rows (individuals) and p columns (categorical variables) |
subcloud |
a vector of logical values and length n. The subcloud of individuals analyzed with class specific MCA is made of the individuals with value |
excl |
nnumeric vector indicating the indexes of the "junk" categories (default is NULL). See |
ncp |
number of dimensions kept in the results (default is 5) |
row.w |
an optional numeric vector of row weights (by default, a vector of 1 for uniform row weights) |
This variant of MCA is used to study a subset of individuals with reference to the whole set of individuals, i.e. to determine the specific features of the subset. It consists in proceeding to the search of the principal axes of the subcloud associated with the subset of individuals (see references).
An object of class csMCA, i.e. a list including:
eig |
a list of vectors containing all the eigenvalues, the percentage of variance, the cumulative percentage of variance, the modified rates and the cumulative modified rates |
call |
a list with informations about input data |
ind |
a list of matrices containing the results for the individuals (coordinates, contributions) |
var |
a list of matrices containing all the results for the categories and variables (weights, coordinates, squared cosines, categories contributions to axes and cloud, test values (v.test), squared correlation ratio (eta2), variable contributions to axes and cloud |
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
# class specific MCA of the subcloud of women # from the Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") female <- Music$Gender=="Women" mca <- csMCA(Music[,1:5], subcloud = female, excl = junk) plot(mca)# class specific MCA of the subcloud of women # from the Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") female <- Music$Gender=="Women" mca <- csMCA(Music[,1:5], subcloud = female, excl = junk) plot(mca)
Descriptive discriminant analysis, aka "Analyse Factorielle Discriminante" for the French school of multivariate data analysis.
DA(data, class, row.w = NULL, type = "FR")DA(data, class, row.w = NULL, type = "FR")
data |
data frame with only numeric variables |
class |
factor specifying the class |
row.w |
numeric vector of row weights. If NULL (default), a vector of 1 for uniform row weights is used. |
type |
If "FR" (default), the inverse of the total covariance matrix is used as metric. If "GB", it is the inverse of the within-class covariance matrix (Mahalanobis metric), which makes the results equivalent to linear discriminant analysis as implemented in |
The results are the same with type "FR" or "GB", only the eigenvalues vary. With type="FR", these eigenvalues vary between 0 and 1 and can be interpreted as "discriminant power".
An object of class PCA from FactoMineR package, with class as qualitative supplementary variable, and one additional item :
cor_ratio |
correlation ratios between |
The code is adapted from a script from Marie Chavent. See: https://marie-chavent.perso.math.cnrs.fr/teaching/
Marie Chavent, Nicolas Robette
Bry X., 1996, Analyses factorielles multiples, Economica.
Lebart L., Morineau A. et Warwick K., 1984, Multivariate Descriptive Statistical Analysis, John Wiley and sons, New-York.)
Saporta G., 2006, Probabilités, analyses des données et statistique, Editions Technip.
library(FactoMineR) data(decathlon) points <- cut(decathlon$Points, c(7300, 7800, 8000, 8120, 8900), c("Q1","Q2","Q3","Q4")) res <- DA(decathlon[,1:10], points) # plot of observations colored by class plot(res, choix = "ind", invisible = "quali", habillage = res$call$quali.sup$numero) # plot of class categories plot(res, choix = "ind", invisible = "ind", col.quali = "darkblue") # plot of variables plot(res, choix = "varcor", invisible = "none")library(FactoMineR) data(decathlon) points <- cut(decathlon$Points, c(7300, 7800, 8000, 8120, 8900), c("Q1","Q2","Q3","Q4")) res <- DA(decathlon[,1:10], points) # plot of observations colored by class plot(res, choix = "ind", invisible = "quali", habillage = res$call$quali.sup$numero) # plot of class categories plot(res, choix = "ind", invisible = "ind", col.quali = "darkblue") # plot of variables plot(res, choix = "varcor", invisible = "none")
Descriptive discriminant analysis (aka "Analyse Factorielle Discriminante" for the French school of multivariate data analysis) with qualitative variables.
DAQ(data, class, excl = NULL, row.w = NULL, type = "FR", select = TRUE)DAQ(data, class, excl = NULL, row.w = NULL, type = "FR", select = TRUE)
data |
data frame with only categorical variables |
class |
factor specifying the class |
excl |
numeric vector indicating the indexes of the "junk" categories (default is NULL). See |
row.w |
numeric vector of row weights. If NULL (default), a vector of 1 for uniform row weights is used. |
type |
character string. If "FR" (default), the inverse of the total covariance matrix is used as metric. If "GB", it is the inverse of the within-class covariance matrix (Mahalanobis metric), which makes the results equivalent to linear discriminant analysis as implemented in |
select |
logical. If TRUE (default), only a selection of components of the MCA are used for the discriminant analysis step. The selected components are those corresponding to eigenvalues higher of equal to 1/Q, with Q the number of variables in |
This approach is also known as "disqual" and was developed by G. Saporta (see references). It consists in two steps : 1. Multiple Correspondence Analysis of the data 2. Discriminant analysis of the components from the MCA
The results are the same with type "FR" or "GB", only the eigenvalues vary. With type="FR", these eigenvalues vary between 0 and 1 and can be interpreted as "discriminant power".
An object of class PCA from FactoMineR package, with class as qualitative supplementary variable and the disjunctive table of data as quantitative supplementary variables, and two additional items :
cor_ratio |
correlation ratios between |
mca |
an object of class |
If there are NAs in data, these NAs will be automatically considered as junk categories. If one desires more flexibility, data should be recoded to add explicit factor levels for NAs and then excl option may be used to select the junk categories.
Nicolas Robette
Bry X., 1996, Analyses factorielles multiples, Economica.
Lebart L., Morineau A. et Warwick K., 1984, Multivariate Descriptive Statistical Analysis, John Wiley and sons, New-York.)
Saporta G., 1977, "Une méthode et un programme d'analyse discriminante sur variables qualitatives", Premières Journées Internationales, Analyses des données et informatiques, INRIA, Rocquencourt.
Saporta G., 2006, Probabilités, analyses des données et statistique, Editions Technip.
library(FactoMineR) data(tea) res <- DAQ(tea[,1:18], tea$SPC) # plot of observations colored by class plot(res, choix = "ind", invisible = "quali", label = "quali", habillage = res$call$quali.sup$numero) # plot of class categories plot(res, choix = "ind", invisible = "ind", col.quali = "black") # plot of the variables in data plot(res, choix = "var", invisible = "var") # plot of the components of the MCA plot(res, choix = "varcor", invisible = "quanti.sup")library(FactoMineR) data(tea) res <- DAQ(tea[,1:18], tea$SPC) # plot of observations colored by class plot(res, choix = "ind", invisible = "quali", label = "quali", habillage = res$call$quali.sup$numero) # plot of class categories plot(res, choix = "ind", invisible = "ind", col.quali = "black") # plot of the variables in data plot(res, choix = "var", invisible = "var") # plot of the components of the MCA plot(res, choix = "varcor", invisible = "quanti.sup")
Dichotomizes the variables in a data frame exclusively composed of categorical variables, i.e. transforms the data into an indicator matrix (also known as disjunctive table)
dichotom(data, out = "numeric")dichotom(data, out = "numeric")
data |
data frame of categorical variables |
out |
character string defining the format for dichotomized variables in the output data frame. Format may be "numeric" (default) or "factor". |
Returns a data frame with dichotomized variables. The number of columns is equal to the total number of categories in the input data.
Nicolas Robette, Julien Barnier
## Dichotomizes Music example data frame data(Music) dic <- dichotom(Music[,1:5]) str(dic) ## with output variables in factor format dic <- dichotom(Music[,1:5], out='factor') str(dic)## Dichotomizes Music example data frame data(Music) dic <- dichotom(Music[,1:5]) str(dic) ## with output variables in factor format dic <- dichotom(Music[,1:5], out='factor') str(dic)
Dichotomizes the factor variables in a data frame composed of mixed format variables, i.e. transforms the factors into an indicator matrix (also known as disjunctive table) and keeps the numerical variables.
dichotomixed(data, out = "numeric")dichotomixed(data, out = "numeric")
data |
data frame of categorical and numerical variables |
out |
character string defining the format for dichotomized variables in the output data frame. Format may be "numeric" (default) or "factor". |
Returns a data frame with numerical variables and dichotomized factor variables
Nicolas Robette
## Dichotomizes Music example data frame data(Music) ## recodes Age as numerical, for the sake of the example Music$Age <- as.numeric(Music$Age) ## dichotomization dic <- dichotomixed(Music) str(dic)## Dichotomizes Music example data frame data(Music) ## recodes Age as numerical, for the sake of the example Music$Age <- as.numeric(Music$Age) ## dichotomization dic <- dichotomixed(Music) str(dic)
Identifies the categories and individuals that contribute the most to each dimension obtained by a Multiple Correspondence Analysis.
dimcontrib(resmca, dim = c(1,2), best = TRUE)dimcontrib(resmca, dim = c(1,2), best = TRUE)
resmca |
object of class |
dim |
numerical vector of the dimensions to describe (default is c(1,2)) |
best |
logical. If FALSE, displays all the categories. If TRUE (default), displays only categories and individuals with contributions higher than average |
Contributions are sorted and assigned a positive or negative sign according to the corresponding categories or individuals coordinates, so as to facilitate interpretation.
Returns a list with the following items :
var |
a list of categories contributions to axes |
ind |
a list of individuals contributions to axes |
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
tabcontrib, dimdescr, dimeta2, dimtypicality
# specific MCA on Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # contributions to axes 1 and 2 dimcontrib(mca)# specific MCA on Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # contributions to axes 1 and 2 dimcontrib(mca)
Identifies the variables and the categories that are the most characteristic according to each dimension obtained by a MCA. It is inspired by dimdesc function in FactoMineR package (see Husson et al, 2010), but allows to analyze variants of MCA, such as specific MCA or class specific MCA.
dimdescr(resmca, vars = NULL, dim = c(1,2), limit = NULL, correlation = "pearson", na.rm.cat = FALSE, na.value.cat = "NA", na.rm.cont = FALSE, nperm = NULL, distrib = "asympt", shortlabs = TRUE)dimdescr(resmca, vars = NULL, dim = c(1,2), limit = NULL, correlation = "pearson", na.rm.cat = FALSE, na.value.cat = "NA", na.rm.cont = FALSE, nperm = NULL, distrib = "asympt", shortlabs = TRUE)
resmca |
object of class |
vars |
data frame of variables to describes the MCA dimensions with. If NULL (default), the active variables of the MCA will be used. |
dim |
the dimensions which are described. Default is c(1,2) |
limit |
for the relationship between a dimension and a categorical variable, only associations (measured with point-biserial correlations) higher or equal to limit will be displayed. If NULL (default), they are all displayed. |
correlation |
character string. The type of correlation measure to be used between two numerical variables : "pearson" (default), "spearman" or "kendall". |
na.rm.cat |
logical, indicating whether NA values in the categorical variables should be silently removed before the computation proceeds. If FALSE (default), an additional level is added to the categorical variables (see na.value.cat argument). |
na.value.cat |
character string. Name of the level for NA category. Default is "NA". Only used if |
na.rm.cont |
logical indicating whether NA values in the numerical variables should be silently removed before the computation proceeds. Default is FALSE. |
nperm |
numeric. Number of permutations for the permutation tests of independence. If NULL (default), no permutation test is performed. |
distrib |
the null distribution of permutation test of independence can be approximated by its asymptotic distribution ( |
shortlabs |
logical. If TRUE (default), the data frame will have short column names, so that all columns can be displayed side by side on a laptop screen. |
See condesc.
Returns a list of ncp lists including:
variables |
associations between dimensions of the MCA and the variables in |
categories |
a data frame with categorical variables from |
Nicolas Robette
Husson, F., Le, S. and Pages, J. (2010). Exploratory Multivariate Analysis by Example Using R, Chapman and Hall.
condesc, dimcontrib, dimeta2, dimtypicality
# specific MCA on Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # description of the dimensions dimdescr(mca, limit = 0.1, nperm = 10)# specific MCA on Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # description of the dimensions dimdescr(mca, limit = 0.1, nperm = 10)
Computes correlation ratios (also known as eta-squared) for a list of supplementary variables of a MCA.
dimeta2(resmca, vars, dim = c(1,2))dimeta2(resmca, vars, dim = c(1,2))
resmca |
object of class |
vars |
a data frame of supplementary variables |
dim |
the axes for which eta2 are computed. Default is c(1,2) |
Returns a data frame with supplementary variables as rows and MCA axes as columns.
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
dimdescr, dimcontrib, dimtypicality
# specific MCA on Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # correlation ratios dimeta2(mca, Music[, c("Gender", "Age")])# specific MCA on Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # correlation ratios dimeta2(mca, Music[, c("Gender", "Age")])
Computes typicality tests for a list of supplementary variables of a MCA.
dimtypicality(resmca, vars, dim = c(1,2), max.pval = 1)dimtypicality(resmca, vars, dim = c(1,2), max.pval = 1)
resmca |
object of class |
vars |
a data frame of supplementary variables |
dim |
the axes for which typicality tests are computed. Default is c(1,2) |
max.pval |
only categories with a p-value lower or equal to |
Returns a list of data frames giving the typicality test statistics and p-values of the supplementary categories for the different axes.
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
# specific MCA on Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # typicality tests for gender and age dimtypicality(mca, Music[, c("Gender", "Age")])# specific MCA on Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # typicality tests for gender and age dimtypicality(mca, Music[, c("Gender", "Age")])
Computes the chi-squared distance between the rows of a data frame of factors.
dist.chi2(X)dist.chi2(X)
X |
data frame. All variables should be factors. |
This function is adapted from chi2Dist function in ExPosition package.
A symmetrical matrix of distances
Nicolas Robette
data(Music) d <- dist.chi2(Music[,1:5]) # a short piece of the distance matrix d[1:3, 1:3]data(Music) d <- dist.chi2(Music[,1:5]) # a short piece of the distance matrix d[1:3, 1:3]
Flips the coordinates of the individuals and the categories on one or more dimensions of a MCA.
flip.mca(resmca, dim = 1)flip.mca(resmca, dim = 1)
resmca |
object of class |
dim |
numerical vector of the dimensions for which the coordinates are flipped. By default, only the first dimension is flipped |
Returns an object of the same class as resmca
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
ggcloud_variables, ggcloud_indiv
# MCA of Music example data set data(Music) mca <- speMCA(Music[,1:5]) ggcloud_variables(mca, legend = "none") # Flips dimensions 1 and 2 flipped_mca <- flip.mca(mca, dim = c(1,2)) ggcloud_variables(flipped_mca, legend = "none")# MCA of Music example data set data(Music) mca <- speMCA(Music[,1:5]) ggcloud_variables(mca, legend = "none") # Flips dimensions 1 and 2 flipped_mca <- flip.mca(mca, dim = c(1,2)) ggcloud_variables(flipped_mca, legend = "none")
Returns a vector of names corresponding the the categories in a data frame exclusively composed of categorical variables.
getindexcat(data)getindexcat(data)
data |
data frame of categorical variables |
This function may be useful prior to a specific MCA, to identify the indexes of the 'junk' categories to exclude.
Returns a character vector with the names of the categories of the variables in the data frame
Nicolas Robette
data(Music) getindexcat(Music[,1:5]) mca <- speMCA(Music[,1:5], excl = c(3,6,9,12,15))data(Music) getindexcat(Music[,1:5]) mca <- speMCA(Music[,1:5], excl = c(3,6,9,12,15))
Adds attractions between categories, as measured by phi coefficients or percentages of maximum deviation (PEM), by plotting segments onto a MCA cloud of variables.
ggadd_attractions(p, resmca, axes = c(1,2), measure = "phi", min.asso = 0.3, col.segment = "lightgray", col.text = "black", text.size = 3)ggadd_attractions(p, resmca, axes = c(1,2), measure = "phi", min.asso = 0.3, col.segment = "lightgray", col.text = "black", text.size = 3)
p |
|
resmca |
object of class |
axes |
numeric vector of length 2, specifying the components (axes) to plot. Default is c(1,2). |
measure |
character string. The measure for attractions: "phi" (default) for phi coefficients, "pem" for percentages of maximum deviation (PEM). |
min.asso |
numerical value ranging from 0 to 1. The minimal attraction value for segments to be plotted. Default is 0.3. |
col.segment |
Character string with the color of the segments. Default is lightgray. |
col.text |
Character string with the color of the labels of the categories. Default is black. |
text.size |
Size of the labels of categories. Default is 3. |
a ggplot2 object
Nicolas Robette
Cibois, Philippe. Les méthodes d’analyse d’enquêtes. Nouvelle édition [en ligne]. Lyon: ENS Éditions, 2014. <http://books.openedition.org/enseditions/1443>
# specific MCA on Taste example data set data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") mca <- speMCA(Taste[,1:11], excl = junk) # Plots attractions p <- ggcloud_variables(mca, col="white", legend="none") ggadd_attractions(p, mca, measure="phi", min.asso=0.1)# specific MCA on Taste example data set data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") mca <- speMCA(Taste[,1:11], excl = junk) # Plots attractions p <- ggcloud_variables(mca, col="white", legend="none") ggadd_attractions(p, mca, measure="phi", min.asso=0.1)
Adds convex hulls for a categorical variable to a MCA cloud of individuals.
ggadd_chulls(p, resmca, var, sel = 1:nlevels(var), axes = c(1,2), prop = 1, alpha = 0.2, label = TRUE, label.size = 5, legend = "right")ggadd_chulls(p, resmca, var, sel = 1:nlevels(var), axes = c(1,2), prop = 1, alpha = 0.2, label = TRUE, label.size = 5, legend = "right")
p |
|
resmca |
object of class |
var |
Factor. The categorical variable used to plot chulls. |
sel |
numeric vector of indexes of the categories to plot (by default, ellipses are plotted for every categories) |
axes |
numeric vector of length 2, specifying the components (axes) to plot. Default is c(1,2). |
prop |
proportion of all the points to be included in the hull (default is 1). |
alpha |
Numerical value from 0 to 1. Transparency of the polygon's fill. Default is O.2 |
label |
Logical. Should the labels of the categories be plotted at the center of chulls ? Default is TRUE. |
label.size |
Size of the labels of the categories at the center of chulls. Default is 5. |
legend |
the position of legends ("none", "left", "right", "bottom", "top", or two-element numeric vector). Default is right. |
a ggplot2 object
Chulls are colored according to the categories of the variable, using the default ggplot2 palette. The palette can be customized using any scale_color_* and scale_fill_* functions, such as scale_color_brewer() and scale_fill_brewer(), scale_color_grey() and scale_fill_grey(), or scale_color_manual() and scale_fill_manual().
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
ggcloud_indiv, ggadd_supvar, ggadd_supvars, ggadd_kellipses, ggadd_ellipses, ggadd_interaction, ggsmoothed_supvar, ggadd_corr, ggadd_density
# specific MCA of Taste example data set data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") mca <- speMCA(Taste[,1:11], excl = junk) # hierarchical clustering # and partition of the individuals into 3 clusters d <- dist(mca$ind$coord[, c(1,2)]) hca <- hclust(d, "ward.D2") cluster <- factor(cutree(hca, 3)) # cloud of individuals # with convex hulls for the clusters. p <- ggcloud_indiv(mca, col = "black") ggadd_chulls(p, mca, cluster)# specific MCA of Taste example data set data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") mca <- speMCA(Taste[,1:11], excl = junk) # hierarchical clustering # and partition of the individuals into 3 clusters d <- dist(mca$ind$coord[, c(1,2)]) hca <- hclust(d, "ward.D2") cluster <- factor(cutree(hca, 3)) # cloud of individuals # with convex hulls for the clusters. p <- ggcloud_indiv(mca, col = "black") ggadd_chulls(p, mca, cluster)
Adds a heatmap representing the correlation coefficients to a MCA cloud of individuals, for a numerical supplementary variable or one category of a categorical supplementary variable.
ggadd_corr(p, resmca, var, cat = levels(var)[1], axes = c(1,2), xbins = 20, ybins = 20, min.n = 1, pal = "RdYlBu", limits = NULL, legend = "right")ggadd_corr(p, resmca, var, cat = levels(var)[1], axes = c(1,2), xbins = 20, ybins = 20, min.n = 1, pal = "RdYlBu", limits = NULL, legend = "right")
p |
|
resmca |
object of class |
var |
factor or numerical vector. The supplementary variable used for the heatmap. |
cat |
character string. The category of |
axes |
numeric vector of length 2, specifying the components (axes) to plot. Default is c(1,2). |
xbins |
integer. Number of bins in the x axis. Default is 20. |
ybins |
integer. Number of bins in the y axis. Default is 20. |
min.n |
integer. Minimal number of points for a tile to be drawn. By default, every tiles are drawn. |
pal |
character string. Name of a (preferably diverging) palette from the |
limits |
numerical vector of length 2. Lower and upper limits of the correlation coefficients for the color scale. Should be centered around 0 for a better view of under/over-representations (for example c(-0.2,0.2)). By default, the maximal absolute value of the correlation coefficients is used. |
legend |
the position of legends ("none", "left", "right", "bottom", "top", or two-element numeric vector). Default is right. |
For each tile of the heatmap, a correlation coefficient is computed between the supplementary variable and the fact of belonging to the tile. This gives a view of the under/over-representation of the supplementary variable according to the position in the cloud of individuals.
a ggplot2 object
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
ggcloud_variables, ggadd_supvar, ggadd_supvars, ggadd_kellipses, ggadd_ellipses, ggadd_interaction, ggsmoothed_supvar, ggadd_chulls, ggadd_density
# specific MCA of Taste example data set data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") mca <- speMCA(Taste[,1:11], excl = junk) # correlation heatmap for Age = 50+ p <- ggcloud_indiv(mca, col = "lightgrey") ggadd_corr(p, mca, var = Taste$Age, cat = "50+", xbins = 10, ybins = 10)# specific MCA of Taste example data set data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") mca <- speMCA(Taste[,1:11], excl = junk) # correlation heatmap for Age = 50+ p <- ggcloud_indiv(mca, col = "lightgrey") ggadd_corr(p, mca, var = Taste$Age, cat = "50+", xbins = 10, ybins = 10)
For a given category of a supplementary variable, adds a layer representing the density of points to the cloud of individuals, either with contours or areas.
ggadd_density(p, resmca, var, cat = levels(var)[1], axes = c(1,2), density = "contour", col.contour = "darkred", pal.area = "viridis", alpha.area = 0.2, ellipse = FALSE)ggadd_density(p, resmca, var, cat = levels(var)[1], axes = c(1,2), density = "contour", col.contour = "darkred", pal.area = "viridis", alpha.area = 0.2, ellipse = FALSE)
p |
|
resmca |
object of class |
var |
factor or numerical vector. The supplementary variable to be plotted. |
cat |
character string. The category of |
axes |
numeric vector of length 2, specifying the components (axes) to plot. Default is c(1,2). |
density |
If "contour" (default), density is plotted with contours. If "area", density is plotted with areas. |
col.contour |
character string. The color of the contours. |
pal.area |
character string. The name of a viridis palette for areas. |
alpha.area |
numeric. Transparency of the areas. Default is 0.2. |
ellipse |
logical. If TRUE, a concentration ellipse is added. |
a ggplot2 object
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
ggcloud_indiv, ggadd_supvar, ggadd_supvars, ggadd_kellipses, ggadd_ellipses, ggadd_interaction, ggsmoothed_supvar, ggadd_chulls, ggadd_corr
# specific MCA of Taste example data set data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") mca <- speMCA(Taste[,1:11], excl = junk) p <- ggcloud_indiv(mca, col='lightgrey') # density plot for Age = 50+ (with contours) ggadd_density(p, mca, var = Taste$Age, cat = "50+") # density plot for Age = 50+ (with contours) ggadd_density(p, mca, var = Taste$Age, cat = "50+", density = "area")# specific MCA of Taste example data set data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") mca <- speMCA(Taste[,1:11], excl = junk) p <- ggcloud_indiv(mca, col='lightgrey') # density plot for Age = 50+ (with contours) ggadd_density(p, mca, var = Taste$Age, cat = "50+") # density plot for Age = 50+ (with contours) ggadd_density(p, mca, var = Taste$Age, cat = "50+", density = "area")
Adds confidence ellipses for a categorical variable to a MCA cloud of individuals
ggadd_ellipses(p, resmca, var, sel = 1:nlevels(var), axes = c(1,2), level = 0.05, label = TRUE, label.size = 3, size = 0.5, points = TRUE, legend = "right")ggadd_ellipses(p, resmca, var, sel = 1:nlevels(var), axes = c(1,2), level = 0.05, label = TRUE, label.size = 3, size = 0.5, points = TRUE, legend = "right")
p |
|
resmca |
object of class |
var |
Factor. The categorical variable used to plot ellipses. |
sel |
numeric vector of indexes of the categories to plot (by default, ellipses are plotted for every categories) |
axes |
numeric vector of length 2, specifying the components (axes) to plot. Default is c(1,2). |
level |
The level at which to draw an ellipse (see |
label |
Logical. Should the labels of the categories be plotted at the center of ellipses ? Default is TRUE. |
label.size |
Size of the labels of the categories at the center of ellipses. Default is 3. |
size |
Size of the lines of the ellipses. Default is 0.5. |
points |
If TRUE (default), the points are coloured according to their subcloud. |
legend |
the position of legends ("none", "left", "right", "bottom", "top", or two-element numeric vector). Default is right. |
A confidence ellipse aims at measuring how the "true" mean point of a category differs from its observed mean point. This is achieved by constructing a confidence zone around the observed mean point. If we choose a conventional level alpha (e.g. 0.05), a (1 - alpha) (e.g. 95 percents) confidence zone is defined as the set of possible mean points that are not significantly different from the observed mean point.
a ggplot2 object
Ellipses are colored according to the categories of the variable, using the default ggplot2 palette. The palette can be customized using any scale_color_* function, such as scale_color_brewer(), scale_color_grey() or scale_color_manual().
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
ggcloud_indiv, ggadd_supvar, ggadd_supvars, ggadd_kellipses, ggadd_density, ggadd_interaction, ggsmoothed_supvar, ggadd_chulls, ggadd_corr
# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # confidence ellipses for Age p <- ggcloud_indiv(mca, col = "lightgrey") ggadd_ellipses(p, mca, Music$Age)# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # confidence ellipses for Age p <- ggcloud_indiv(mca, col = "lightgrey") ggadd_ellipses(p, mca, Music$Age)
Adds the interactions between two categorical supplementary variables to a MCA cloud of variables
ggadd_interaction(p, resmca, v1, v2, sel1 = 1:nlevels(v1), sel2 = 1:nlevels(v2), axes = c(1,2), textsize = 5, legend = "right")ggadd_interaction(p, resmca, v1, v2, sel1 = 1:nlevels(v1), sel2 = 1:nlevels(v2), axes = c(1,2), textsize = 5, legend = "right")
p |
|
resmca |
object of class |
v1 |
Factor. The first categorical supplementary variable. |
v2 |
Factor. The second categorical supplementary variable. |
sel1 |
Numeric vector of indexes of the categories of the first supplementary variable to be used in interaction. By default, every categories are used. |
sel2 |
Numeric vector of indexes of the categories of the second supplementary variable to be used in interaction. By default, every categories are used. |
axes |
numeric vector of length 2, specifying the components (axes) to plot. Default is c(1,2). |
textsize |
Size of the labels of categories. Default is 5. |
legend |
the position of legends ("none", "left", "right", "bottom", "top", or two-element numeric vector). Default is right. |
a ggplot2 object
Lines and labels are colored according to the variables, using the default ggplot2 palette. The palette can be customized using any scale_color_* function, such as scale_color_brewer(), scale_color_grey() or scale_color_manual().
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
ggcloud_variables, ggadd_supvar, ggadd_supvars, ggadd_kellipses, ggadd_ellipses, ggadd_corr, ggsmoothed_supvar, ggadd_chulls, ggadd_density
# specific MCA of Taste example data set data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") mca <- speMCA(Taste[,1:11], excl = junk) # interaction between Gender and Age p <- ggcloud_variables(mca, col = "lightgrey", shapes = FALSE) ggadd_interaction(p, mca, Taste$Gender, Taste$Age)# specific MCA of Taste example data set data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") mca <- speMCA(Taste[,1:11], excl = junk) # interaction between Gender and Age p <- ggcloud_variables(mca, col = "lightgrey", shapes = FALSE) ggadd_interaction(p, mca, Taste$Gender, Taste$Age)
Adds concentration ellipses and other kinds of k-inertia ellipses for a categorical variable to a MCA cloud of individuals.
ggadd_kellipses(p, resmca, var, sel = 1:nlevels(var), axes = c(1,2), kappa = 2, label = TRUE, label.size = 3, size = 0.5, points = TRUE, legend = "right")ggadd_kellipses(p, resmca, var, sel = 1:nlevels(var), axes = c(1,2), kappa = 2, label = TRUE, label.size = 3, size = 0.5, points = TRUE, legend = "right")
p |
|
resmca |
object of class |
var |
Factor. The categorical variable used to plot ellipses. |
sel |
numeric vector of indexes of the categories to plot (by default, ellipses are plotted for every categories) |
axes |
numeric vector of length 2, specifying the components (axes) to plot. Default is c(1,2). |
kappa |
numeric. The kappa value (i.e. "index") of the inertia ellipses. By default, kappa = 2, which means that concentration ellipses are plotted. |
label |
Logical. Should the labels of the categories be plotted at the center of ellipses ? Default is TRUE. |
label.size |
Size of the labels of the categories at the center of ellipses. Default is 3. |
size |
Size of the lines of the ellipses. Default is 0.5. |
points |
If TRUE (default), the points are coloured according to their subcloud. |
legend |
the position of legends ("none", "left", "right", "bottom", "top", or two-element numeric vector). Default is right. |
If kappa=2, ellipses are called "concentration" ellipses and, for a normally shaped subcloud, contain 86.47 percents of the points of the subcloud. If kappa=1, ellipses are "indicator" ellipses and contain 39.35 percents of the points of the subcloud. If kappa=1.177, ellipses are "median" ellipses and contain 50 percents of the points of the subcloud. This function has to be used after the cloud of individuals has been drawn.
a ggplot2 object
Ellipses are colored according to the categories of the variable, using the default ggplot2 palette. The palette can be customized using any scale_color_* function, such as scale_color_brewer(), scale_color_grey() or scale_color_manual().
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
ggcloud_indiv, ggadd_supvar, ggadd_supvars, ggadd_ellipses, ggadd_density, ggadd_interaction, ggsmoothed_supvar, ggadd_chulls, ggadd_corr
# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # concentration ellipses for Age p <- ggcloud_indiv(mca, col = "lightgrey") ggadd_ellipses(p, mca, Music$Age)# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # concentration ellipses for Age p <- ggcloud_indiv(mca, col = "lightgrey") ggadd_ellipses(p, mca, Music$Age)
Adds supplementary individuals to a MCA cloud of the individuals
ggadd_supind(p, resmca, dfsup, axes = c(1,2), col = "black", textsize = 5, pointsize = 2)ggadd_supind(p, resmca, dfsup, axes = c(1,2), col = "black", textsize = 5, pointsize = 2)
p |
|
resmca |
object of class |
dfsup |
data frame with the supplementary individuals. It must have the same factors as the data frame used as input for the initial MCA. |
axes |
numeric vector of length 2, specifying the dimensions (axes) to plot (default is c(1,2)) |
col |
color for the labels and points of the individuals (default is black) |
textsize |
Size of the labels of the individuals. Default is 5. |
pointsize |
Size of the points of the individuals. If NULL, only labels are plotted. Default is 2. |
The function uses the row names of dfsup as labels for the individuals.
Nicolas Robette
# specific MCA of Music example data set data(Music) rownames(Music) <- paste0("i", 1:nrow(Music)) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # adds individuals 1, 20 and 300 as supplementary individuals # onto the cloud of individuals p <- ggcloud_indiv(mca, col = "lightgrey") ggadd_supind(p, mca, Music[c(1,20,300), 1:5])# specific MCA of Music example data set data(Music) rownames(Music) <- paste0("i", 1:nrow(Music)) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # adds individuals 1, 20 and 300 as supplementary individuals # onto the cloud of individuals p <- ggcloud_indiv(mca, col = "lightgrey") ggadd_supind(p, mca, Music[c(1,20,300), 1:5])
Adds a categorical supplementary variable to a MCA cloud of variables.
ggadd_supvar(p, resmca, var, sel = 1:nlevels(var), axes = c(1,2), col = "black", shape = 1, prop = NULL, textsize = 3, shapesize = 6, segment = FALSE, vname = NULL)ggadd_supvar(p, resmca, var, sel = 1:nlevels(var), axes = c(1,2), col = "black", shape = 1, prop = NULL, textsize = 3, shapesize = 6, segment = FALSE, vname = NULL)
p |
|
resmca |
object of class |
var |
Factor. The categorical supplementary variable. It does not need to have been used at the MCA step. |
sel |
Numeric vector of indexes of the categories of the supplementary variable to be added to the plot. By default, labels are plotted for every categories. |
axes |
numeric vector of length 2, specifying the components (axes) to plot. Default is c(1,2). |
col |
Character. Color of the shapes and labels of the categories. Default is black. |
shape |
Symbol to be used in addition the the labels of categories (default is 1). If NULL, only labels are plotted. |
prop |
If NULL, the size of the labels (if shape=NULL) or the shapes (otherwise) is constant. If 'n', the size is proportional the the weights of categories; if 'vtest1', the size is proportional to the test values of the categories on the first dimension of the plot; if 'vtest2', the size is proportional to the test values of the categories on the second dimension of the plot; if 'cos1', the size is proportional to the cosines of the categories on the first dimension of the plot; if 'cos2', the size is proportional to the cosines of the categories on the second dimension of the plot; if 'cos12', the size is proportional to the total cosines of the categories on the two dimensions of the plot. |
textsize |
Size of the labels of categories if shape is not NULL, or if shape=NULL and prop=NULL. Default is 3. |
shapesize |
Size of the shapes if prop=NULL, maximum size of the shapes in other cases. Default is 6. |
segment |
Logical. Should one add lines between categories ? Default is FALSE. |
vname |
A character string to be used as a prefix for the labels of the categories. If NULL (default), no prefix is added. |
a ggplot2 object
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
ggcloud_variables, ggadd_supvars, ggadd_ellipses, ggadd_kellipses, ggadd_density, ggadd_interaction, ggsmoothed_supvar, ggadd_chulls, ggadd_corr
# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # adds Age as a supplementary variable # onto the cloud of variables p <- ggcloud_variables(mca, col = "lightgrey", shapes = FALSE) ggadd_supvar(p, mca, Music$Age, segment = TRUE)# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # adds Age as a supplementary variable # onto the cloud of variables p <- ggcloud_variables(mca, col = "lightgrey", shapes = FALSE) ggadd_supvar(p, mca, Music$Age, segment = TRUE)
Adds categorical supplementary variables to a MCA cloud of variables.
ggadd_supvars(p, resmca, vars, excl = NULL, points = "all", min.cos2 = 0.1, axes = c(1,2), col = NULL, shapes = FALSE, prop = NULL, textsize = 3, shapesize = 6, vlab = TRUE, vname = NULL, force = 1, max.overlaps = Inf)ggadd_supvars(p, resmca, vars, excl = NULL, points = "all", min.cos2 = 0.1, axes = c(1,2), col = NULL, shapes = FALSE, prop = NULL, textsize = 3, shapesize = 6, vlab = TRUE, vname = NULL, force = 1, max.overlaps = Inf)
p |
|
resmca |
object of class |
vars |
A data frame of categorical supplementary variables. All these variables should be factors. |
excl |
character vector of supplementary categories to exclude from the plot, specified in the form "namevariable.namecategory" (for instance "Gender.Men"). If NULL (default), all the supplementary categories are plotted. |
points |
character string. If 'all' all categories are plotted (default); if 'besth' only those with a minimum squared cosine on horizontal axis are plotted; if 'bestv' only those with a minimum squared cosine on vertical axis are plotted; if 'besthv' only those with a minimum squared cosine on horizontal or vertical axis are plotted; if 'best' only those with a minimum squared cosine on the plane are plotted. |
min.cos2 |
numerical value. The minimal squared cosine if 'points' argument is different from 'all'. Default |
axes |
numeric vector of length 2, specifying the components (axes) to plot. Default is c(1,2). |
col |
character string. Color name for the labels (and the shapes if |
shapes |
Logical. If TRUE, symbols are used in addition to the labels of categories. Default is FALSE. |
prop |
If NULL, the size of the labels (if |
textsize |
Size of the labels of categories if |
shapesize |
Size of the shapes if |
vlab |
Logical. If TRUE (default), the variable name is added as a prefix for the labels of the categories. |
vname |
deprecated, use vlab instead |
force |
Force of repulsion between overlapping text labels. Defaults to 1. If 0, labels are not repelled at all. |
max.overlaps |
Exclude text labels that overlap too many things. Defaults to Inf, which means no labels are excluded. |
a ggplot2 object
Shapes and labels are colored according to the categories of the variable, using the default ggplot2 palette. The palette can be customized using any scale_color_* function, such as scale_color_brewer(), scale_color_grey() or scale_color_manual().
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
ggcloud_variables, ggadd_supvar, ggadd_ellipses, ggadd_kellipses, ggadd_density, ggadd_interaction, ggsmoothed_supvar, ggadd_chulls, ggadd_corr
# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # adds several supplementary variables # onto the cloud of variables p <- ggcloud_variables(mca, col = "lightgrey", shapes = FALSE) ggadd_supvars(p, mca, Music[, c("Gender","Age")]) # the same, excluding men ggadd_supvars(p, mca, Music[, c("Gender","Age")], excl = "Gender.Men") # the same, keeping only categories # with cos2 >= 0.001 for dimension 1 ggadd_supvars(p, mca, Music[, c("Gender","Age")], points = "besth", min.cos2 = 0.001)# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # adds several supplementary variables # onto the cloud of variables p <- ggcloud_variables(mca, col = "lightgrey", shapes = FALSE) ggadd_supvars(p, mca, Music[, c("Gender","Age")]) # the same, excluding men ggadd_supvars(p, mca, Music[, c("Gender","Age")], excl = "Gender.Men") # the same, keeping only categories # with cos2 >= 0.001 for dimension 1 ggadd_supvars(p, mca, Music[, c("Gender","Age")], points = "besth", min.cos2 = 0.001)
Plots variables on a single axis of a Multiple Correspondence Analysis. Variables can be active or supplementary.
ggaxis_variables(resmca, var = NULL, axis = 1, prop = NULL, underline = FALSE, col = NULL, vlab = TRUE)ggaxis_variables(resmca, var = NULL, axis = 1, prop = NULL, underline = FALSE, col = NULL, vlab = TRUE)
resmca |
object of class |
var |
If NULL (default), all the active variables of the MCA are plotted. If a character string, the named active variables of the MCA is plotted. If a factor, it is plotted as a supplementary variable. |
axis |
numeric value. The MCA axis to plot. Default is 1. |
prop |
If NULL (default), the size of the labels is constant. If "freq", the size is proportional to the weights of categories. If "ctr", it's proportional to the contributions of categories (only used for active variables). If "cos2", it's proportional to the squared cosines of the categories. If "pval", it's proportional to 1 minus the p-values of typicality tests (only used for supplementary variables). If "cor", it's proportional to the point biserial correlation of the categories (only used for supplementary variables). |
underline |
logical. If TRUE, the labels of the categories with contributions above average are underlined. Default is FALSE. Only used for active variables. |
col |
character string. Color name for the labels of the categories. If NULL and |
vlab |
Logical. Should the variable names be used as a prefix for the labels of the categories. Default is TRUE. |
a ggplot2 object
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
# specific MCA of Taste example data set data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") mca <- speMCA(Taste[,1:11], excl = junk) # plots all the active categories on axis 1 ggaxis_variables(mca) # the same with other plotting options ggaxis_variables(mca, prop = "freq", underline = TRUE, col = "black") # plots Active variable Classical on axis 1 ggaxis_variables(mca, var = "Classical", axis = 1, prop = "ctr", underline = TRUE) # plots supplementary variable Educ on axis 1 ggaxis_variables(mca, var = Taste$Educ, axis = 1, prop = "pval")# specific MCA of Taste example data set data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") mca <- speMCA(Taste[,1:11], excl = junk) # plots all the active categories on axis 1 ggaxis_variables(mca) # the same with other plotting options ggaxis_variables(mca, prop = "freq", underline = TRUE, col = "black") # plots Active variable Classical on axis 1 ggaxis_variables(mca, var = "Classical", axis = 1, prop = "ctr", underline = TRUE) # plots supplementary variable Educ on axis 1 ggaxis_variables(mca, var = Taste$Educ, axis = 1, prop = "pval")
Ellipses for bootstrap validation of MCA, through the computation of the coordinates of supplementary variables for bootstrap replications of the data.
ggbootvalid_supvars(resmca, vars = NULL, axes = c(1,2), K = 30, ellipse = "norm", level = 0.95, col = NULL, active = FALSE, legend = "right")ggbootvalid_supvars(resmca, vars = NULL, axes = c(1,2), K = 30, ellipse = "norm", level = 0.95, col = NULL, active = FALSE, legend = "right")
resmca |
object of class |
vars |
A data frame of categorical supplementary variables. All these variables should be factors. |
axes |
numeric vector of length 2, specifying the components (axes) to plot. Default is c(1,2). |
K |
integer. Number of bootstrap replications (default is 30). |
ellipse |
character string. The type of ellipse. The default "norm" assumes a multivariate normal distribution, "t" assumes a multivariate t-distribution, and "euclid" draws a circle with the radius equal to level, representing the euclidean distance from the center. |
level |
numerical value. The level at which to draw an ellipse, or, if |
col |
Character string. Color name for the ellipses and labels of the categories. If NULL (default), the default |
active |
logical. If TRUE, the labels of active variables are added to the plot in lightgray. Default is FALSE. |
legend |
the position of legends ("none", "left", "right", "bottom", "top", or two-element numeric vector). Default is right. |
The bootstrap technique is used here as an internal (and non-parametric) validation procedure of the results of a multiple correspondence analysis. For supplementary variables, only partial bootstrap is possible. The partial bootstrap does not compute new MCAs: it projects bootstrap replications of the initial data as supplementary elements of the MCA. See references for more details.
The default parameters for ellipses assume a multivariate normal distribution drawn at level 0.95.
a ggplot2 object
If col argument is NULL, ellipses and labels are colored according to the variables, using the default ggplot2 palette. The palette can be customized using any scale_color_* function, such as scale_color_brewer(), scale_color_grey() or scale_color_manual().
Nicolas Robette
Lebart L. (2006). "Validation Techniques in Multiple Correspondence Analysis". In M. Greenacre et J. Blasius (eds), Multiple Correspondence Analysis and related techniques, Chapman and Hall/CRC, p.179-196.
Lebart L. (2007). "Which bootstrap for principal axes methods?". In P. Brito et al. (eds), Selected Contributions in Data Analysis and Classification, Springer, p.581-588.
bootvalid_supvars, ggbootvalid_variables
# specific MCA of Taste example data set data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") mca <- speMCA(Taste[,1:11], excl = junk) # bootstrap validation ellipses # for three supplementary variables sup <- Taste[,c("Gender", "Age", "Educ")] ggbootvalid_supvars(mca, sup)# specific MCA of Taste example data set data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") mca <- speMCA(Taste[,1:11], excl = junk) # bootstrap validation ellipses # for three supplementary variables sup <- Taste[,c("Gender", "Age", "Educ")] ggbootvalid_supvars(mca, sup)
Ellipses for bootstrap validation of MCA, through the computation of the coordinates of active variables for bootstrap replications of the data.
ggbootvalid_variables(resmca, axes = c(1,2), type = "partial", K = 30, ellipse = "norm", level = 0.95, col = NULL, legend = "right")ggbootvalid_variables(resmca, axes = c(1,2), type = "partial", K = 30, ellipse = "norm", level = 0.95, col = NULL, legend = "right")
resmca |
object of class |
axes |
numeric vector of length 2, specifying the components (axes) to plot. Default is c(1,2). |
type |
character string. Can be "partial", "total1", "total2" or "total3" (see details). Default is "partial". |
K |
integer. Number of bootstrap replications (default is 30). |
ellipse |
character string. The type of ellipse. The default "norm" assumes a multivariate normal distribution, "t" assumes a multivariate t-distribution, and "euclid" draws a circle with the radius equal to level, representing the euclidean distance from the center. |
level |
numerical value. The level at which to draw an ellipse, or, if |
col |
Character string. Color name for the ellipses and labels of the categories. If NULL (default), the default |
legend |
the position of legends ("none", "left", "right", "bottom", "top", or two-element numeric vector). Default is right. |
The bootstrap technique is used here as an internal (and non-parametric) validation procedure of the results of a multiple correspondence analysis. Following the work of Lebart, several methods are proposed. The total bootstrap uses new MCAs computed from bootstrap replications of the initial data. In the type 1 bootstrap (type = "total1"), the sign of the coordinates is corrected if necessary (the direction of the axes of an ACM being arbitrary). In type 2 (type = "total2"), the order of the axes and the sign of the coordinates are corrected if necessary. In type 3 (type = "total3"), a procrustean rotation is used to find the best superposition between the initial axes and the replicated axes.
The partial bootstrap (type = "partial") does not compute new MCAs: it projects bootstrap replications of the initial data as supplementary elements of the MCA. It gives a more optimistic view of the stability of the results than the total bootstrap. It is also faster. See references for more details, pros and cons of the various types, etc.
The default parameters for ellipses assume a multivariate normal distribution drawn at level 0.95.
a ggplot2 object
If col argument is NULL, ellipses and labels are colored according to the variables, using the default ggplot2 palette. The palette can be customized using any scale_color_* function, such as scale_color_brewer(), scale_color_grey() or scale_color_manual().
Nicolas Robette
Lebart L. (2006). "Validation Techniques in Multiple Correspondence Analysis". In M. Greenacre et J. Blasius (eds), Multiple Correspondence Analysis and related techniques, Chapman and Hall/CRC, p.179-196.
Lebart L. (2007). "Which bootstrap for principal axes methods?". In P. Brito et al. (eds), Selected Contributions in Data Analysis and Classification, Springer, p.581-588.
bootvalid_variables , ggbootvalid_supvars
# specific MCA of Taste example data set data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") mca <- speMCA(Taste[,1:11], excl = junk) # bootstrap validation ellipses for active variables ggbootvalid_variables(mca, type = "partial", K = 5)# specific MCA of Taste example data set data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") mca <- speMCA(Taste[,1:11], excl = junk) # bootstrap validation ellipses for active variables ggbootvalid_variables(mca, type = "partial", K = 5)
Plots a Multiple Correspondence Analysis cloud of individuals.
ggcloud_indiv(resmca, type = "i", points = "all", axes = c(1,2), col = "dodgerblue4", point.size = 0.5, alpha = 0.6, repel = FALSE, text.size = 2, density = NULL, col.contour = "darkred", hex.bins = 50, hex.pal = "viridis")ggcloud_indiv(resmca, type = "i", points = "all", axes = c(1,2), col = "dodgerblue4", point.size = 0.5, alpha = 0.6, repel = FALSE, text.size = 2, density = NULL, col.contour = "darkred", hex.bins = 50, hex.pal = "viridis")
resmca |
object of class |
type |
If 'i', points are plotted. If 'inames', labels of individuals are plotted. |
points |
character string. If 'all' all points are plotted (default). If 'besth' only those who contribute most to horizontal axis are plotted. If 'bestv' only those who contribute most to vertical axis are plotted. If 'besthv' only those who contribute most to horizontal or vertical axis are plotted. If 'best' only those who contribute most to the plane are plotted. |
axes |
numeric vector of length 2, specifying the components (axes) to plot. Default is c(1,2). |
col |
If a factor, points or labels are colored according to their category regarding this factor. If a string with color name, every points or labels have the same color. Default is "dodgerblue4". |
point.size |
Size of the points of individuals. Default is 0.5. |
alpha |
Transparency of the points or labels of individuals. Default is 0.6. |
repel |
Logical. When |
text.size |
Size of the labels of individuals. Default is 2. |
density |
If NULL (default), no density layer is added. If "contour", density is plotted with contours. If "hex", density is plotted with hexagon bins. |
col.contour |
character string. The color of the contours. Only used if density="contour". |
hex.bins |
integer. The number of bins in both vertical and horizontal directions. Only used if |
hex.pal |
character string. The name of a viridis palette for hexagon bins. Only used if |
Sometimes the dots are too many and overlap. It is then difficult to get an accurate idea of the distribution of the cloud of individuals. The density argument allows you to add an additional layer to represent the density of points in the plane, in the form of contours or hexagonal areas.
a ggplot2 object
If col argument is a factor, points or labels are colored according to the categories of the factor, using the default ggplot2 palette. The palette can be customized using any scale_color_* function, such as scale_color_brewer(), scale_color_grey() or scale_color_manual().
Anton Perdoncin, Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
# specific MCA of Taste example data set data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") mca <- speMCA(Taste[,1:11], excl = junk) # cloud of individuals ggcloud_indiv(mca) # points are colored according to gender ggcloud_indiv(mca, col=Taste$Gender) # a density layer of contours is added ggcloud_indiv(mca, density = "contour") # a density layer of hexagon bins is added ggcloud_indiv(mca, density = "hex", hex.bin = 10)# specific MCA of Taste example data set data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") mca <- speMCA(Taste[,1:11], excl = junk) # cloud of individuals ggcloud_indiv(mca) # points are colored according to gender ggcloud_indiv(mca, col=Taste$Gender) # a density layer of contours is added ggcloud_indiv(mca, density = "contour") # a density layer of hexagon bins is added ggcloud_indiv(mca, density = "hex", hex.bin = 10)
Plots a Multiple Correspondence Analysis cloud of variables.
ggcloud_variables(resmca, axes = c(1,2), points = "all", min.ctr = NULL, max.pval = 0.01, face = "pp", shapes = TRUE, prop = NULL, textsize = 3, shapesize = 3, col = NULL, col.by.group = TRUE, alpha = 1, segment.alpha = 0.5, vlab = TRUE, sep = ".", legend = "right", force = 1, max.overlaps = Inf)ggcloud_variables(resmca, axes = c(1,2), points = "all", min.ctr = NULL, max.pval = 0.01, face = "pp", shapes = TRUE, prop = NULL, textsize = 3, shapesize = 3, col = NULL, col.by.group = TRUE, alpha = 1, segment.alpha = 0.5, vlab = TRUE, sep = ".", legend = "right", force = 1, max.overlaps = Inf)
resmca |
object of class |
axes |
numeric vector of length 2, specifying the components (axes) to plot. Default is c(1,2). |
points |
character string. If 'all' all categories are plotted (default); if 'besth' only those who contribute most to horizontal axis are plotted; if 'bestv' only those who contribute most to vertical axis are plotted; if 'besthv' only those who contribute most to horizontal or vertical axis are plotted; if 'best' only those who contribute most to the plane are plotted. |
min.ctr |
Numerical value between 0 and 100. The minimum contribution (in percent) for a category to be displayed if the |
max.pval |
Numerical value between 0 and 100. The maximal p-value derived from test-values for a category to be displayed if the |
face |
character string. Changes the face of the category labels when their contribution is greater than |
shapes |
Logical. Should shapes be plotted for categories (in addition to labels) ? Default is TRUE. |
prop |
If NULL, the size of the labels (if shapes=FALSE) or the shapes (if shapes=TRUE) is constant. If 'n', the size is proportional the the weights of categories; if 'ctr1', the size is proportional to the contributions of the categories on the first dimension of the plot; if 'ctr2', the size is proportional to the contributions of the categories on the second dimension of the plot; if 'ctr12', the size is proportional to the contributions of the categories on the plane ; if 'ctr.cloud', the size is proportional to the total contributions of the categories on the whole cloud; if 'cos1', the size is proportional to the quality of representation (squared cosines) of the categories on the first dimension of the plot; if 'cos2', the size is proportional to the quality of representation of the categories on the second dimension of the plot; if 'cos12', the size is proportional to the quality of representation of the categories on the plane; if 'vtest1', the size is proportional to the test-values of the categories on the first dimension of the plot; if 'vtest2', the size is proportional to the test-values of the categories on the second dimension of the plot. |
textsize |
Size of the labels of categories if shapes=TRUE, or if shapes=FALSE and prop=NULL. Default is 3. |
shapesize |
Size if the shapes of categories if shapes=TRUE and prop=FALSE. Default is 3. |
col |
Character string. Color name for the shapes and labels of the categories. If NULL (default), the default |
col.by.group |
Logical. If |
alpha |
Transparency of the shapes and labels of categories. Default is 1. |
segment.alpha |
Transparency of the line segment beside labels of categories. Default is 0.5. |
vlab |
Logical. Should the variable names be used as a prefix for the labels of the categories. Default is TRUE. |
sep |
Character string used as a separator if vlab=TRUE. |
legend |
the position of legends ("none", "left", "right", "bottom", "top", or two-element numeric vector). Default is right. |
force |
Force of repulsion between overlapping text labels. Defaults to 1. If 0, labels are not repelled at all. |
max.overlaps |
Exclude text labels that overlap too many things. Defaults to Inf, which means no labels are excluded. |
a ggplot2 object
If col argument is NULL, shapes or labels are colored according to the variables, using the default ggplot2 palette. The palette can be customized using any scale_color_* function, such as scale_color_brewer(), scale_color_grey() or scale_color_manual().
If resmca is of type stMCA or multiMCA and points is not equal to "all", test-values are used instead of contributions (which are not available for these MCA variants) to select the most important categories ; if points is equal to best, only categories with high test-values for horizontal axis or vertical axis are plotted.
Anton Perdoncin, Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # cloud of variables ggcloud_variables(mca) # cloud of variables with only categories contributing the most ggcloud_variables(mca, points = "best", prop = "n") # cloud of variables with other plotting options ggcloud_variables(mca, shapes = FALSE, legend = "none", col = "black", face = "ui")# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # cloud of variables ggcloud_variables(mca) # cloud of variables with only categories contributing the most ggcloud_variables(mca, points = "best", prop = "n") # cloud of variables with other plotting options ggcloud_variables(mca, shapes = FALSE, legend = "none", col = "black", face = "ui")
Plots the eta-squared (squared correlation ratios) of the active variables of a MCA.
ggeta2_variables(resmca, axes = c(1,2))ggeta2_variables(resmca, axes = c(1,2))
resmca |
object of class |
axes |
numeric vector of length 2, specifying the components (axes) to plot. Default is c(1,2). |
This plot was proposed by Escofier and Pagès (2008) under the name "carré des liaisons", i.e. square of relationships, using correlation ratios to measure these relationships. Eta-squared (i.e. correlation ratio) is a measure of global association between a continuous variable and a categorical variable : it measures the share of variance of the continuous variables "explained" by the categorical variable. Here, it is used to plot the association between the active variables and the axes of the MCA cloud.
a ggplot2 object
Nicolas Robette
Escofier B. and Pagès J., 2008, Analyses factorielles simples et multiples, Dunod.
ggcloud_variables, ggadd_attractions
data(Music) junk <- c("FrenchPop.NA","Rap.NA","Jazz.NA","Classical.NA","Rock.NA") mca <- speMCA(Music[,1:5], excl = junk) ggeta2_variables(mca)data(Music) junk <- c("FrenchPop.NA","Rap.NA","Jazz.NA","Classical.NA","Rock.NA") mca <- speMCA(Music[,1:5], excl = junk) ggeta2_variables(mca)
Plots the density of a supplementary variable in a MCA space, using a grid, smoothing and interpolation (via inverse distance weighting.)
ggsmoothed_supvar(resmca, var, cat, axes = c(1,2), center = FALSE, scale = FALSE, nc = c(20, 20), power = 2, limits = NULL, pal = "RdBu")ggsmoothed_supvar(resmca, var, cat, axes = c(1,2), center = FALSE, scale = FALSE, nc = c(20, 20), power = 2, limits = NULL, pal = "RdBu")
resmca |
object of class |
var |
factor or numeric vector. The supplementary variable to be plotted. |
cat |
character string. If |
axes |
numeric vector of length 2, specifying the components (axes) to plot. Default is c(1,2). |
center |
logical. Whether the supplementary variable should be centered or not. Default is FALSE. |
scale |
logical. Whether the supplementary variable should be scaled to unit variance or not. Default is FALSE. |
nc |
integer vector of length 2. Number of grid cells in x and y direction (columns, rows). |
power |
numerical value. The power to use in weight calculation for inverse distance weighting. Default is 2. |
limits |
numerical vector of length 2. Lower and upper limit of the scale for the supplementary variable. |
pal |
character string. Name of a (preferably diverging) palette from the |
The construction of the plot takes place in several steps. First, the two-dimensional MCA space is cut into a grid of hexagonal cells. Then, for each cell, the average value of the supplementary variable is calculated for the observations located in that cell (if the variable is numerical), or the proportion of observations belonging to the category studied (if the variable is categorical). The results are interpolated and smoothed to make the plot easier to read, using the inverse distance weighting technique, which is very common in spatial analysis.
The supplementary variable can be centered beforehand, to represent deviations from the mean (for a numerical variable) or from the mean proportion (for a categorical variable). It can also be scaled to measure deviations in numbers of standard deviations, which can be useful for comparing the results of several supplementary variables.
a ggplot2 object
Nicolas Robette
Shepard, Donald (1968). "A two-dimensional interpolation function for irregularly-spaced data". Proceedings of the 1968 ACM National Conference. pp. 517–524. doi:10.1145/800186.810616
ggadd_supvar, ggadd_supvars, ggadd_kellipses, ggadd_ellipses, ggadd_interaction, ggadd_corr, ggadd_chulls, ggadd_density
# specific MCA of Taste example data set data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") mca <- speMCA(Taste[,1:11], excl = junk) # density plot for Educ = "High" ggsmoothed_supvar(mca, Taste$Educ, "High") # centered and scaled density plot for Age ggsmoothed_supvar(mca, as.numeric(Taste$Age), center = TRUE, scale = TRUE)# specific MCA of Taste example data set data(Taste) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA", "Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA", "Musical.NA") mca <- speMCA(Taste[,1:11], excl = junk) # density plot for Educ = "High" ggsmoothed_supvar(mca, Taste$Educ, "High") # centered and scaled density plot for Age ggsmoothed_supvar(mca, as.numeric(Taste$Age), center = TRUE, scale = TRUE)
Generalized Principal Component Analysis
gPCA(X, row.w = NULL, col.w = NULL, center = FALSE, scale = FALSE, tol = 1e-07)gPCA(X, row.w = NULL, col.w = NULL, center = FALSE, scale = FALSE, tol = 1e-07)
X |
data frame of active variables |
row.w |
numeric vector of row weights. If NULL (default), a vector of 1 for uniform row weights is used. |
col.w |
numeric vector of column weights. If NULL (default), a vector of 1 for uniform column weights is used. |
center |
logical. If TRUE, variables are centered (default is FALSE). |
scale |
logical. If TRUE, variables are scaled to unit variance (default is FALSE). |
tol |
a tolerance threshold for null eigenvalues (a value less than |
Generalized PCA is basically a PCA with the possibility to specify row weights (i.e. "masses") and variable weights (i.e. the "metric"), and to choose whether to center and scale the variables. This flexibility makes it the building block of many variants of PCA, such as Correspondence Analysis and Multiple Correspondence Analysis.
Generalized PCA is also known as "biweighted PCA", "duality diagram" or "generalized singular value decomposition".
An object of class PCA from FactoMineR package
Nicolas Robette
Bry X., 1995, Analyses factorielles simples, Economica.
Escofier B. and Pagès J., Analyses factorielles simples et multiples, Dunod (2008).
Escoufier, Y. (1987) The duality diagram : a means of better practical applications In Development in numerical ecology, Legendre, P. & Legendre, L. (Eds.) NATO advanced Institute, Serie G. Springer Verlag, Berlin, 139–156.
library(FactoMineR) data(decathlon) res <- gPCA(decathlon[,1:10], center = TRUE, scale = TRUE) plot(res, choix = "var")library(FactoMineR) data(decathlon) res <- gPCA(decathlon[,1:10], center = TRUE, scale = TRUE) plot(res, choix = "var")
From MCA results, computes a homogeneity test between categories of a supplementary variable, i.e. characterizes the homogeneity of several subclouds.
homog.test(resmca, var, dim = c(1,2))homog.test(resmca, var, dim = c(1,2))
resmca |
object of class |
var |
the categorical supplementary variable. It does not need to have been used at the MCA step. |
dim |
the axes which are described. Default is c(1,2) |
Returns a list of lists, one for each selected dimension in the MCA. Each list has 2 elements :
test.stat |
The square matrix of test statistics |
p.values |
The square matrix of p-values |
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
supvar, supvars, dimtypicality
# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # homogeneity test for variable Age homog.test(mca, Music$Age)# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # homogeneity test for variable Age homog.test(mca, Music$Age)
This function launches a shiny app to define interactively the junk categories before a specific MCA.
ijunk(data, init_junk = NULL)ijunk(data, init_junk = NULL)
data |
data frame of categorical variables to be used as active in a specific MCA |
init_junk |
optional vector of junk categories. Can be a numeric vector indicating the indexes of the junk categories or a character vector of junk categories, specified in the form "namevariable.namecategory" (for instance "gender.male"). Default is NULL. |
Once the selection of junk categories is interactively done, the function provides the code to use in a script. It also offer the opportunity to select a set of junk categories at once by writing the common suffix of these categories.
A character vector of junk categories
Nicolas Robette
## Not run: data(Music) ijunk(Music[,1:5]) # or junk <- ijunk(Music[,1:5]) # To update an existing vector of junk categories junk <- ijunk(Music[,1:5], init_junk = c("Rock.NA", "Rap.NA")) # and then mca <- speMCA(Music[,1:5], excl = junk) ## End(Not run)## Not run: data(Music) ijunk(Music[,1:5]) # or junk <- ijunk(Music[,1:5]) # To update an existing vector of junk categories junk <- ijunk(Music[,1:5], init_junk = c("Rock.NA", "Rap.NA")) # and then mca <- speMCA(Music[,1:5], excl = junk) ## End(Not run)
Multiple Correspondence Analysis with Instrumental Variables
MCAiv(Y, X, excl = NULL, row.w = NULL, ncp = 5)MCAiv(Y, X, excl = NULL, row.w = NULL, ncp = 5)
Y |
data frame with only factors |
X |
data frame of instrumental variables, which can be numeric or factors. It must have the same number of rows as |
excl |
numeric vector indicating the indexes of the "junk" categories (default is NULL). See |
row.w |
Numeric vector of row weights. If NULL (default), a vector of 1 for uniform row weights is used. |
ncp |
number of dimensions kept in the results (by default 5) |
Multiple Correspondence Analysis with Instrumental Variables consists in three steps :
1. Specific MCA of Y, keeping all the dimensions of the space
2. Computation of one linear regression for each dimension in the specific MCA, with individual coordinates as response and all variables in X as explanatory variables.
3. Principal Component Analysis of the set of predicted values from the regressions in 2.
Multiple Correspondence Analysis with Instrumental Variables is also known as "Canonical Correspondence Analysis" or "Constrained Correspondence Analysis".
An object of class PCA from FactoMineR package, with Y and X as supplementary variables, and an additional item :
ratio |
the share of inertia explained by the instrumental variables |
.
If there are NAs in Y, these NAs will be automatically considered as junk categories. If one desires more flexibility, Y should be recoded to add explicit factor levels for NAs and then excl option may be used to select the junk categories.
Nicolas Robette
Bry X., 1996, Analyses factorielles multiples, Economica.
Lebart L., Morineau A. et Warwick K., 1984, Multivariate Descriptive Statistical Analysis, John Wiley and sons, New-York.)
library(FactoMineR) data(tea) # MCAIV of tea data # with age, sex, SPC and Sport as instrumental variables mcaiv <- MCAiv(tea[,1:18], tea[,19:22]) mcaiv$ratio plot(mcaiv, choix = "ind", invisible = "ind", col.quali = "black")library(FactoMineR) data(tea) # MCAIV of tea data # with age, sex, SPC and Sport as instrumental variables mcaiv <- MCAiv(tea[,1:18], tea[,19:22]) mcaiv$ratio plot(mcaiv, choix = "ind", invisible = "ind", col.quali = "black")
Multiple Correspondence Analysis with Orthogonal Instrumental Variables
MCAoiv(X, Z, excl = NULL, row.w = NULL, ncp = 5)MCAoiv(X, Z, excl = NULL, row.w = NULL, ncp = 5)
X |
data frame with only factors |
Z |
data frame of instrumental variables, which can be numeric or factors. It must have the same number of rows as |
excl |
numeric vector indicating the indexes of the "junk" categories (default is NULL). See |
row.w |
Numeric vector of row weights. If NULL (default), a vector of 1 for uniform row weights is used. |
ncp |
number of dimensions kept in the results (by default 5) |
Multiple Correspondence Analysis with Orthogonal Instrumental Variables consists in three steps :
1. Specific MCA of Y, keeping all the dimensions of the space
2. Computation of one linear regression for each dimension in the specific MCA, with individual coordinates as response and all variables in X as explanatory variables.
3. Principal Component Analysis of the set of residuals from the regressions in 2.
An object of class PCA from FactoMineR package, with X as supplementary variables, and an additional item :
ratio |
the share of inertia not explained by the instrumental variables |
.
If there are NAs in Y, these NAs will be automatically considered as junk categories. If one desires more flexibility, Y should be recoded to add explicit factor levels for NAs and then excl option may be used to select the junk categories.
Nicolas Robette
Bry X., 1996, Analyses factorielles multiples, Economica.
Lebart L., Morineau A. et Warwick K., 1984, Multivariate Descriptive Statistical Analysis, John Wiley and sons, New-York.)
library(FactoMineR) data(tea) mcaoiv <- MCAoiv(tea[,1:18], tea[,19:22]) mcaoiv$ratio plot(mcaoiv, choix = "ind", invisible = "ind", col.quali = "black")library(FactoMineR) data(tea) mcaoiv <- MCAoiv(tea[,1:18], tea[,19:22]) mcaoiv$ratio plot(mcaoiv, choix = "ind", invisible = "ind", col.quali = "black")
Computes the medoids of a cluster solution.
medoids(D, cl)medoids(D, cl)
D |
square distance matrix (n rows * n columns, i.e. n individuals) or |
cl |
vector with the clustering solution (its length should be n) |
A medoid is a representative object of a cluster whose average dissimilarity to all the objects in the cluster is minimal. Medoids are always members of the data set (contrary to means or centroids).
Returns a numeric vector with the indexes of medoids.
Nicolas Robette
Kaufman, L. and Rousseeuw, P.J. (1990). Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York.
Anja Struyf, Mia Hubert & Peter J. Rousseeuw (1996). "Clustering in an Object-Oriented Environment". Journal of Statistical Software.
dist, cluster, hclust, cutree , pam
# hierarchical clustering of the Music example data set, # partition into 3 groups # and then computation of the medoids. data(Music) temp <- dichotom(Music[,1:5]) d <- dist(temp) clus <- cutree(hclust(d), 3) medoids(d, clus)# hierarchical clustering of the Music example data set, # partition into 3 groups # and then computation of the medoids. data(Music) temp <- dichotom(Music[,1:5]) d <- dist(temp) clus <- cutree(hclust(d), 3) medoids(d, clus)
Computes Benzecri's modified rates of variance of a multiple correspondence analysis.
modif.rate(resmca)modif.rate(resmca)
resmca |
object of class |
As MCA clouds often have a high dimensionality, the variance rates of the first principle axes may be quite low, which makes them hard to interpret. Benzecri (1992, p.412) proposed to use modified rates to better appreciate the relative importance of the principal axes.
Returns a list of two data frames.
The first one is called raw and has 3 variables:
eigen |
eigen values |
rate |
rates |
cum.rate |
cumulative rates |
The second one is called modif and has 2 variables:
mrate |
modified rates |
cum.mrate |
cumulative modified rates |
Nicolas Robette
Benzecri J.P., Correspondence analysis handbook, New-York: Dekker (1992).
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
# MCA of Music' example data set data(Music) mca <- speMCA(Music[,1:5]) # modified rates of variance modif.rate(mca)# MCA of Music' example data set data(Music) mca <- speMCA(Music[,1:5]) # modified rates of variance modif.rate(mca)
Performs Multiple Factor Analysis, drawing on the work of Escofier and Pages (1994). It allows the use of MCA variants (e.g. specific MCA or class specific MCA) as inputs.
multiMCA(l_mca, ncp = 5, compute.rv = FALSE)multiMCA(l_mca, ncp = 5, compute.rv = FALSE)
l_mca |
a list of objects of class |
ncp |
number of dimensions kept in the results (default is 5) |
compute.rv |
whether RV coefficients should be computed or not (default is FALSE, which makes the function execute faster) |
This function binds individual coordinates from every MCA in l_mca argument, weights them by the first eigenvalue, and the resulting data frame is used as input for Principal Component Analysis (PCA).
Returns an object of class multiMCA, i.e. a list:
eig |
a list of numeric vector for eigenvalues, percentage of variance and cumulative percentage of variance |
var |
a list of matrices with results for input MCAs components (coordinates, correlations between variables and axes, squared cosines, contributions) |
ind |
a list of matrices with results for individuals (coordinates, squared cosines, contributions) |
call |
a list with informations about input data |
VAR |
a list of matrices with results for categories and variables in the input MCAs (coordinates, squared cosines, test-values, variances) |
my.mca |
lists the content of the objects in |
RV |
a matrix of RV coefficients |
Nicolas Robette
Escofier, B. and Pages, J. (1994) "Multiple Factor Analysis (AFMULT package)". Computational Statistics and Data Analysis, 18, 121-140.
data(Taste) # specific MCA on music variables of Taste example data set mca1 <- speMCA(Taste[,1:5], excl = c(3,6,9,12,15)) # specific MCA on movie variables of Taste example data set mca2 <- speMCA(Taste[,6:11], excl = c(3,6,9,12,15,18)) # Multiple Factor Analysis of the two sets of variables mfa <- multiMCA(list(mca1,mca2)) plot.multiMCA(mfa)data(Taste) # specific MCA on music variables of Taste example data set mca1 <- speMCA(Taste[,1:5], excl = c(3,6,9,12,15)) # specific MCA on movie variables of Taste example data set mca2 <- speMCA(Taste[,6:11], excl = c(3,6,9,12,15,18)) # Multiple Factor Analysis of the two sets of variables mfa <- multiMCA(list(mca1,mca2)) plot.multiMCA(mfa)
The data concerns tastes for music of a set of 500 individuals. It contains 5 variables of likes for music genres (french pop, rap, rock, jazz and classical), 2 variables about music listening and 2 additional variables (gender and age).
data(Music)data(Music)
A data frame with 500 observations and the following 7 variables:
FrenchPopfactor with levels No, Yes, NA
Rapfactor with levels No, Yes, NA
Rockfactor with levels No, Yes, NA
Jazzfactor with levels No, Yes, NA
Classicalfactor with levels No, Yes, NA
Genderfactor with levels Men, Women
Agefactor with levels 15-24, 25-49, 50+
OnlyMusfactor with levels Daily, Often, Rare, Never, indicating how often one only listens to music.
Dailyis a factor with levels No, Yes indicating if one listens to music every day.
NA stands for "not available"
data(Music) str(Music)data(Music) str(Music)
Nonsymmetric correspondence analysis, for analysing contingency tables with a dependence structure
nsCA(X, ncp = 5, row.sup = NULL, col.sup = NULL, quanti.sup = NULL, quali.sup = NULL, graph = FALSE, axes = c(1,2), row.w = NULL)nsCA(X, ncp = 5, row.sup = NULL, col.sup = NULL, quanti.sup = NULL, quali.sup = NULL, graph = FALSE, axes = c(1,2), row.w = NULL)
X |
a data frame or a table with n rows and p columns, i.e. a contingency table. Predictor variable should be in rows and response variable in columns. |
ncp |
number of dimensions kept in the results (by default 5) |
row.sup |
a vector indicating the indexes of the supplementary rows |
col.sup |
a vector indicating the indexes of the supplementary columns |
quanti.sup |
a vector indicating the indexes of the supplementary continuous variables |
quali.sup |
a vector indicating the indexes of the categorical supplementary variables |
graph |
boolean, if TRUE a graph is displayed |
axes |
a length 2 vector specifying the components to plot |
row.w |
an optional row weights (by default, a vector of 1 and each row has a weight equals to its margin); the weights are given only for the active rows |
When dealing with a contingency table with a dependence structure, i.e. when the role of the two variables is not symmetrical but, on the contrary, one can be considered as predicting the other, nonsymmetric correspondence analysis (NSCA) can be used to represent the predictive structure in the table and to assess the predictive power of the predictor variable.
Technically, NSCA is very similar to the standard CA, the main difference being that the columns of the contingency table are not weighted by their rarity (i.e. the inverse of the marginal frequencies).
An object of class CA from FactoMineR package, with an additional item :
GK.tau |
Goodman and Kruskal tau |
The code is adapted from the CA function in FactoMineR package.
Nicolas Robette
Kroonenberg P.M. and Lombardo R., 1999, "Nonsymmetric Correspondence Analysis: A Tool for Analysing Contingency Tables with a Dependence Structure", Multivariate Behavioral Research, 34 (3), 367-396.
data(Music) # The combination of Gender and Age is the predictor variable # "Focused" listening to music is the response variable tab <- with(Music, table(interaction(Gender, Age), OnlyMus)) nsca <- nsCA(tab) nsca.biplot(nsca) # Goodman and Kruskal tau nsca$GK.taudata(Music) # The combination of Gender and Age is the predictor variable # "Focused" listening to music is the response variable tab <- with(Music, table(interaction(Gender, Age), OnlyMus)) nsca <- nsCA(tab) nsca.biplot(nsca) # Goodman and Kruskal tau nsca$GK.tau
Biplot for Nonsymmetric correspondence analysis, for analysing contingency tables with a dependence structure
nsca.biplot(nsca, axes = c(1,2))nsca.biplot(nsca, axes = c(1,2))
nsca |
an object of class |
axes |
numeric vector of length 2, specifying the components (axes) to plot. Default is c(1,2). |
The biplots of an NSCA reflect the dependency structure of the contingency table and thus should not be interpreted as the planes of a standard CA. A first principle is that the graph displays the centred row profiles. A second principle is that the relationships between rows and columns are contained in their inner products : the rows are depicted as vectors, also called biplot axes, and the columns are projected on these vectors. If some columns have projections on the row vector far away from the origin, then the row has a comparatively large increase in predictability, and its profile deviates considerably from the marginal one, especially for that column.
For more detailed interpretational guidelines, see Kroonenberg and Lombardo (1999, pp.377-378).
a ggplot2 object
Nicolas Robette
Kroonenberg P.M. and Lombardo R., 1999, "Nonsymmetric Correspondence Analysis: A Tool for Analysing Contingency Tables with a Dependence Structure", Multivariate Behavioral Research, 34 (3), 367-396.
data(Music) # The combination of Gender and Age is the predictor variable # "Focused" listening to music is the response variable tab <- with(Music, table(interaction(Gender, Age), OnlyMus)) nsca <- nsCA(tab) nsca.biplot(nsca) # Goodman and Kruskal tau nsca$GK.taudata(Music) # The combination of Gender and Age is the predictor variable # "Focused" listening to music is the response variable tab <- with(Music, table(interaction(Gender, Age), OnlyMus)) nsca <- nsCA(tab) nsca.biplot(nsca) # Goodman and Kruskal tau nsca$GK.tau
Principal Component Analysis with Instrumental Variables
PCAiv(Y, X, row.w = NULL, ncp = 5)PCAiv(Y, X, row.w = NULL, ncp = 5)
Y |
data frame with only numeric variables |
X |
data frame of instrumental variables, which can be numeric or factors. It must have the same number of rows as |
row.w |
Numeric vector of row weights. If NULL (default), a vector of 1 for uniform row weights is used. |
ncp |
number of dimensions kept in the results (by default 5) |
Principal Component Analysis with Instrumental Variables consists in two steps :
1. Computation of one linear regression for each variable in Y, with this variable as response and all variables in X as explanatory variables.
2. Principal Component Analysis of the set of predicted values from the regressions in 1 ("Y hat").
Principal Component Analysis with Instrumental Variables is also known as "redundancy analysis"
An object of class PCA from FactoMineR package, with X as supplementary variables, and an additional item :
ratio |
the share of inertia explained by the instrumental variables |
.
Nicolas Robette
Bry X., 1996, Analyses factorielles multiples, Economica.
Lebart L., Morineau A. et Warwick K., 1984, Multivariate Descriptive Statistical Analysis, John Wiley and sons, New-York.)
library(FactoMineR) data(decathlon) # PCAiv of decathlon data set # with Points and Competition as instrumental variables pcaiv <- PCAiv(decathlon[,1:10], decathlon[,12:13]) pcaiv$ratio # plot of \code{Y} variables + quantitative instrumental variables (here Points) plot(pcaiv, choix = "var") # plot of qualitative instrumental variables (here Competition) plot(pcaiv, choix = "ind", invisible = "ind", col.quali = "black")library(FactoMineR) data(decathlon) # PCAiv of decathlon data set # with Points and Competition as instrumental variables pcaiv <- PCAiv(decathlon[,1:10], decathlon[,12:13]) pcaiv$ratio # plot of \code{Y} variables + quantitative instrumental variables (here Points) plot(pcaiv, choix = "var") # plot of qualitative instrumental variables (here Competition) plot(pcaiv, choix = "ind", invisible = "ind", col.quali = "black")
Principal Component Analysis with Orthogonal Instrumental Variables
PCAoiv(X, Z, row.w = NULL, ncp = 5)PCAoiv(X, Z, row.w = NULL, ncp = 5)
X |
data frame with only numeric variables |
Z |
data frame of instrumental variables to be "partialled out"", which can be numeric or factors. It must have the same number of rows as |
row.w |
Numeric vector of row weights. If NULL (default), a vector of 1 for uniform row weights is used. |
ncp |
number of dimensions kept in the results (by default 5) |
Principal Component Analysis with Orthogonal Instrumental Variables consists in two steps :
1. Computation of one linear regression for each variable in X, with this variable as response and all variables in Z as explanatory variables.
2. Principal Component Analysis of the set of residuals from the regressions in 1.
An object of class PCA from FactoMineR package, and an additional item :
ratio |
the share of inertia not explained by the instrumental variables |
.
Nicolas Robette
Bry X., 1996, Analyses factorielles multiples, Economica.
Lebart L., Morineau A. et Warwick K., 1984, Multivariate Descriptive Statistical Analysis, John Wiley and sons, New-York.)
library(FactoMineR) data(decathlon) pcaoiv <- PCAoiv(decathlon[,1:10], decathlon[,12:13]) plot(pcaoiv, choix = "var", invisible = "quanti.sup")library(FactoMineR) data(decathlon) pcaoiv <- PCAoiv(decathlon[,1:10], decathlon[,12:13]) plot(pcaoiv, choix = "var", invisible = "quanti.sup")
For a given plane of a MCA, computes contributions and squared cosines of the active variables and categories and of the active individuals.
planecontrib(resmca, axes = c(1,2))planecontrib(resmca, axes = c(1,2))
resmca |
object of class |
axes |
numeric vector of length 2, specifying the axes forming the plane to describe. Default is c(1,2). |
A list of two lists. The first deals with variables :
ctr |
vector of contributions of the active categories to the plane |
cos2 |
vector of squared cosines of the active categories in the plane |
vctr |
vector of contributions of the active variables to the plane |
The second deals with observations :
ctr |
vector of contributions of the observations to the plane |
cos2 |
vector of squared cosines of the observations in the plane |
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
data(Music) junk <- c("FrenchPop.NA","Rap.NA","Jazz.NA","Classical.NA","Rock.NA") mca <- speMCA(Music[,1:5], excl = junk) co <- planecontrib(mca) co$vardata(Music) junk <- c("FrenchPop.NA","Rap.NA","Jazz.NA","Classical.NA","Rock.NA") mca <- speMCA(Music[,1:5], excl = junk) co <- planecontrib(mca) co$var
Plots a class specific Multiple Correspondence Analysis (resulting from csMCA function), i.e. the clouds of individuals or categories.
## S3 method for class 'csMCA' plot(x, type = "v", axes = 1:2, points = "all", col = "dodgerblue4", app = 0, ...)## S3 method for class 'csMCA' plot(x, type = "v", axes = 1:2, points = "all", col = "dodgerblue4", app = 0, ...)
x |
object of class |
type |
character string: 'v' to plot the categories (default), 'i' to plot individuals' points, 'inames' to plot individuals' names |
axes |
numeric vector of length 2, specifying the components (axes) to plot (c(1,2) is default) |
points |
character string. If 'all' all points are plotted (default); if 'besth' only those who contribute most to horizontal axis are plotted; if 'bestv' only those who contribute most to vertical axis are plotted; if 'besthv' only those who contribute most to horizontal or vertical axis are plotted. |
col |
color for the points of the individuals or for the labels of the categories (default is 'dodgerblue4') |
app |
numerical value. If 0 (default), only the labels of the categories are plotted and their size is constant; if 1, only the labels are plotted and their size is proportional to the weights of the categories; if 2, points (triangles) and labels are plotted, and points size is proportional to the weight of the categories. |
... |
further arguments passed to or from other methods, such as cex, cex.main, ... |
A category is considered to be one of the most contributing to a given axis if its contribution is higher than the average contribution, i.e. 100 divided by the total number of categories.
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
csMCA, textvarsup, conc.ellipse
# class specific MCA on Music example data set # ignoring every NA values categories # and focusing on the subset of women, data(Music) female <- Music$Gender=="Women" junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- csMCA(Music[,1:5], subcloud = female, excl = junk) # cloud of categories plot(mca) # cloud of most contributing categories plot(mca,axes=c(2,3), points = "besthv", col = "darkred", app = 1)# class specific MCA on Music example data set # ignoring every NA values categories # and focusing on the subset of women, data(Music) female <- Music$Gender=="Women" junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- csMCA(Music[,1:5], subcloud = female, excl = junk) # cloud of categories plot(mca) # cloud of most contributing categories plot(mca,axes=c(2,3), points = "besthv", col = "darkred", app = 1)
Plots Multiple Factor Analysis data, resulting from multiMCA function.
## S3 method for class 'multiMCA' plot(x, type = "v", axes = c(1, 2), points = "all", threshold = 2.58, groups = 1:x$call$ngroups, col = rainbow(x$call$ngroups), app = 0, ...)## S3 method for class 'multiMCA' plot(x, type = "v", axes = c(1, 2), points = "all", threshold = 2.58, groups = 1:x$call$ngroups, col = rainbow(x$call$ngroups), app = 0, ...)
x |
object of class |
type |
character string: 'v' to plot the categories (default), 'i' to plot individuals' points, 'inames' to plot individuals' names |
axes |
numeric vector of length 2, specifying the components (axes) to plot (c(1,2) is default) |
points |
character string. If 'all' all points are plotted (default); if 'besth' only those who are the most correlated to horizontal axis are plotted; if 'bestv' only those who are the most correlated to vertical axis are plotted; if 'best' only those who are the most coorelated to horizontal or vertical axis are plotted. |
threshold |
numeric value. V-test minimal value for the selection of plotted categories. |
groups |
numeric vector specifying the groups of categories to plot. By default, every groups of categories will be plotted |
col |
a color for the points of the individuals or a vector of colors for the labels of the groups of categories (by default, rainbow palette is used) |
app |
numerical value. If 0 (default), only the labels of the categories are plotted and their size is constant; if 1, only the labels are plotted and their size is proportional to the weights of the categories; if 2, points (triangles) and labels are plotted, and points size is proportional to the weight of the categories. |
... |
further arguments passed to or from other methods, such as cex, cex.main, ... |
A category is considered to be one of the most correlated to a given axis if its test-value is higher then 2.58 (which corresponds to a 0.05 threshold).
Nicolas Robette
Escofier, B. and Pages, J. (1994) "Multiple Factor Analysis (AFMULT package)". Computational Statistics and Data Analysis, 18, 121-140.
multiMCA, textvarsup, speMCA, csMCA
# specific MCA on music variables of Taste example data set ## another one on movie variables of 'Taste' example data set, ## and then a Multiple Factor Analysis and plots the results. data(Taste) # specific MCA on music variables of Taste example data set mca1 <- speMCA(Taste[,1:5], excl = c(3,6,9,12,15)) # specific MCA on movie variables of Taste example data set mca2 <- speMCA(Taste[,6:11], excl = c(3,6,9,12,15,18)) # Multiple Factor Analysis mfa <- multiMCA(list(mca1,mca2)) # plot plot.multiMCA(mfa, col = c("darkred", "darkblue")) # plot of the second set of variables (movie) plot.multiMCA(mfa, groups = 2, app = 1)# specific MCA on music variables of Taste example data set ## another one on movie variables of 'Taste' example data set, ## and then a Multiple Factor Analysis and plots the results. data(Taste) # specific MCA on music variables of Taste example data set mca1 <- speMCA(Taste[,1:5], excl = c(3,6,9,12,15)) # specific MCA on movie variables of Taste example data set mca2 <- speMCA(Taste[,6:11], excl = c(3,6,9,12,15,18)) # Multiple Factor Analysis mfa <- multiMCA(list(mca1,mca2)) # plot plot.multiMCA(mfa, col = c("darkred", "darkblue")) # plot of the second set of variables (movie) plot.multiMCA(mfa, groups = 2, app = 1)
Plots a specific Multiple Correspondence Analysis (resulting from speMCA function), i.e. the clouds of individuals or categories.
## S3 method for class 'speMCA' plot(x, type = "v", axes = c(1,2), points = "all", col = "dodgerblue4", app = 0, ...)## S3 method for class 'speMCA' plot(x, type = "v", axes = c(1,2), points = "all", col = "dodgerblue4", app = 0, ...)
x |
object of class |
type |
character string: 'v' to plot the categories (default), 'i' to plot individuals' points, 'inames' to plot individuals' names |
axes |
numeric vector of length 2, specifying the components (axes) to plot (c(1,2) is default) |
points |
character string. If 'all' all points are plotted (default); if 'besth' only those who contribute most to horizontal axis are plotted; if 'bestv' only those who contribute most to vertical axis are plotted; if 'besthv' only those who contribute most to horizontal or vertical axis are plotted; if 'best' only those who contribute most to the plane are plotted. |
col |
color for the points of the individuals or for the labels of the categories (default is 'dodgerblue4') |
app |
numerical value. If 0 (default), only the labels of the categories are plotted and their size is constant; if 1, only the labels are plotted and their size is proportional to the weights of the categories; if 2, points (triangles) and labels are plotted, and points size is proportional to the weight of the categories. |
... |
further arguments passed to or from other methods, such as cex, cex.main, ... |
A category is considered to be one of the most contributing to a given axis if its contribution is higher than the average contribution, i.e. 100 divided by the total number of categories.
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
speMCA, textvarsup, conc.ellipse
# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # cloud of categories plot(mca)# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # cloud of categories plot(mca)
Plots a standardized Multiple Correspondence Analysis (resulting from stMCA function), i.e. the clouds of individuals or categories.
## S3 method for class 'stMCA' plot(x, type = "v", axes = 1:2, points = "all", threshold = 2.58, groups=NULL, col = "dodgerblue4", app = 0, ...)## S3 method for class 'stMCA' plot(x, type = "v", axes = 1:2, points = "all", threshold = 2.58, groups=NULL, col = "dodgerblue4", app = 0, ...)
x |
object of class |
type |
character string: 'v' to plot the categories (default), 'i' to plot individuals' points, 'inames' to plot individuals' names |
axes |
numeric vector of length 2, specifying the components (axes) to plot (c(1,2) is default) |
points |
character string. If 'all' all points are plotted (default); if 'besth' only those who are the most correlated to horizontal axis are plotted; if 'bestv' only those who are the most correlated to vertical axis are plotted; if 'best' only those who are the most coorelated to horizontal or vertical axis are plotted. |
threshold |
numeric value. V-test minimal value for the selection of plotted categories. |
groups |
only if x$call$input.mca = 'multiMCA', i.e. if the MCA standardized to x object was a |
col |
color for the points of the individuals or for the labels of the categories (default is 'dodgerblue4') |
app |
numerical value. If 0 (default), only the labels of the categories are plotted and their size is constant; if 1, only the labels are plotted and their size is proportional to the weights of the categories; if 2, points (triangles) and labels are plotted, and points size is proportional to the weight of the categories. |
... |
further arguments passed to or from other methods, such as cex, cex.main, ... |
A category is considered to be one of the most correlated to a given axis if its test-value is higher then 2.58 (which corresponds to a 0.05 threshold).
Nicolas Robette
Bry X., Robette N., Roueff O., 2016, « A dialogue of the deaf in the statistical theater? Adressing structural effects within a geometric data analysis framework », Quality & Quantity, 50(3), pp 1009–1020 [https://link.springer.com/article/10.1007/s11135-015-0187-z]
stMCA, textvarsup, conc.ellipse
# standardized MCA of Music example data set # controlling for age ## and then draws the cloud of categories. data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) stmca <- stMCA(mca, control = list(Music$Age)) # cloud of categories plot(stmca) # cloud of categories on dimensions 2 and 3 plot(stmca, axes = c(2,3), points = "best", col = "darkred", app = 1)# standardized MCA of Music example data set # controlling for age ## and then draws the cloud of categories. data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) stmca <- stMCA(mca, control = list(Music$Age)) # cloud of categories plot(stmca) # cloud of categories on dimensions 2 and 3 plot(stmca, axes = c(2,3), points = "best", col = "darkred", app = 1)
Computes the quadrant of active individuals from a MCA.
quadrant(resmca, dim = c(1,2))quadrant(resmca, dim = c(1,2))
resmca |
object of class |
dim |
dimensions of the space (default is c(1,2)) |
Returns a factor with four levels : upper_left, lower_left, upper_right, lower_right
Nicolas Robette
# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # distribution of the quadrants table(quadrant(mca, c(1,2)))# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # distribution of the quadrants table(quadrant(mca, c(1,2)))
Transforms a symmetrical contingency table so that it can be used for quasi-correspondence analysis, also called correspondence analysis of incomplete contingency table.
quasindep(tab, order = 3, tol = 1e-6)quasindep(tab, order = 3, tol = 1e-6)
tab |
a symmetric table or matrix |
order |
numeric value. Order of reconstitution of the quasi-independence data. Default is 3. |
tol |
numeric value. The tolerance threshold to be considered for convergence to null during iteration process. Default is 1e-6. |
In order to carry out a "quasi-correspondence analysis", also called "correspondence analysis of incomplete table", the principle is to stop analyzing the differences between the observed data and the situation of independence between the variable in rows and the variable in columns, as it is the case in the classical correspondence analysis, and to consider the differences between the data and a situation of quasi-independence, i.e. independence for some cells of the table only. In the most common situation, it is therefore a matter of applying the independence hypothesis to the off-diagonal cells only and replacing the diagonal with values that do not influence the analysis. Such values are obtained in an iterative way by replacing the numbers of the cells of the diagonal by their third order reconstruction, then by recalculating the correspondence analysis until convergence is reached. The algorithm used is developed in van der Heijden (1992: 11-12).
An object of the same class and dimensions as tab : the quasi-independence data to be analyzed with Correspondence Analysis.
This function is adapted from Milan Bouchet-Valat's script in the supplementary material of his article indicated in the reference section.
De Leeuw J et van der Heijden PGM (1985) Quasi-Correspondence Analysis. Leiden: University of Leiden.
Van der Heijden PGM (1992) Three Approaches to Study the Departure from Quasi-independence. Statistica Applicata 4: 465-80.
Bouchet-Valat M (2015) L'analyse statistique des tables de contingence carrées - L'homogamie socioprofessionnelle en France - I, L'analyse des correspondances Bulletin de Méthodologie Sociologique 125: 65–88. <doi:10.1177/0759106314555655>
## Not run: tab <- matrix(c(165,49,70,100,48,223, 6,201,226,212,90,216, 4,96,446,214,72,77, 5,84,305,317,126,188, 3,52,151,190,110,189, 17,234,310,601,309,1222), nrow = 6, ncol = 6, byrow = TRUE) newtab <- quasindep(tab) ## End(Not run)## Not run: tab <- matrix(c(165,49,70,100,48,223, 6,201,226,212,90,216, 4,96,446,214,72,77, 5,84,305,317,126,188, 3,52,151,190,110,189, 17,234,310,601,309,1222), nrow = 6, ncol = 6, byrow = TRUE) newtab <- quasindep(tab) ## End(Not run)
Computes the RV coefficient between two groups of numerical variables.
rvcoef(Xa, Xb, row.w = NULL)rvcoef(Xa, Xb, row.w = NULL)
Xa |
data frame with the first group of numerical variables |
Xb |
data frame with the second group of numerical variables |
row.w |
numeric vector of row weights. If NULL (default), a vector of 1 for uniform row weights is used. |
Xa and Xb should have the same number of rows.
numerical value : the RV coefficient
Nicolas Robette
Escouffier, Y. (1973) Le traitement des variables vectorielles. Biometrics 29 751–760.
# RV coefficient between decathlon results by sport # and Rank and Points library(FactoMineR) data(decathlon) Xa <- decathlon[,1:10] Xb <- decathlon[,11:12] str(Xa) str(Xb) rvcoef(Xa, Xb)# RV coefficient between decathlon results by sport # and Rank and Points library(FactoMineR) data(decathlon) Xa <- decathlon[,1:10] Xb <- decathlon[,11:12] str(Xa) str(Xb) rvcoef(Xa, Xb)
From MCA results, computes scaled deviations between categories for a categorical supplementary variable.
scaled.dev(resmca, var)scaled.dev(resmca, var)
resmca |
object of class |
var |
the categorical supplementary variable. It does not need to have been used at the MCA step. |
Returns a list with one matrix for each dimension of the MCA. Each matrix is filled with scaled deviations between the categories of the supplementary variable, for a given dimension.
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
supvar, supvars, ggadd_supvar, ggadd_supvars, textvarsup, supind
# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # computes scaled deviations for Age supplementary variable scaled.dev(mca,Music$Age)# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # computes scaled deviations for Age supplementary variable scaled.dev(mca,Music$Age)
Performs a specific Multiple Correspondence Analysis, i.e. a variant of MCA that allows to treat undesirable categories as passive categories.
speMCA(data, excl = NULL, ncp = 5, row.w = NULL)speMCA(data, excl = NULL, ncp = 5, row.w = NULL)
data |
data frame with n rows (individuals) and p columns (categorical variables) |
excl |
numeric vector indicating the indexes of the "junk" categories (default is NULL). See |
ncp |
number of dimensions kept in the results (default is 5) |
row.w |
an optional numeric vector of row weights. If NULL (default), a vector of 1 for uniform row weights) |
Undesirable (i.e. "junk") categories may be of several kinds: infrequent categories (say, <5 percents), heterogeneous categories (e.g. "others") or uninterpretable categories (e.g. "not available"). In these cases, specific MCA may be useful to ignore these categories for the determination of distances between individuals (see references).
If there are NAs in data, these NAs will be automatically considered as junk categories. If one desires more flexibility, data should be recoded to add explicit factor levels for NAs and then excl option may be used to select the junk categories.
Returns an object of class speMCA, i.e. a list including:
eig |
a list of vectors containing all the eigenvalues, the percentage of variance, the cumulative percentage of variance, the modified rates and the cumulative modified rates |
call |
a list with informations about input data |
ind |
a list of matrices containing the results for the individuals (coordinates, contributions, squared cosines and total distances) |
var |
a list of matrices containing all the results for the categories and variables (weights, coordinates, squared cosines, categories contributions to axes and cloud, test values (v.test), squared correlation ratio (eta2), variable contributions to axes and cloud, total distances |
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
getindexcat, ijunk, plot.speMCA, ggcloud_indiv, ggcloud_variables, csMCA
# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # This is equivalent to : mca <- speMCA(Music[,1:5], excl = c(3,6,9,12,15))# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # This is equivalent to : mca <- speMCA(Music[,1:5], excl = c(3,6,9,12,15))
Performs a standardized Multiple Correspondence Analysis, i.e it takes MCA results and forces all the dimensions to be orthogonal to a supplementary "control" variable.
stMCA(resmca, control)stMCA(resmca, control)
resmca |
an object of class |
control |
a list of control variables |
Standardized MCA unfolds in several steps. 1. First, for each dimension of an input MCA, individual coordinates are used as dependent variable in a linear regression model and the 'control' variable is included as covariate in the same model. 2. The residuals from every models are retained and bound together. The resulting data frame is composed of continuous variables and its number of columns is equal to the number of dimensions in the input MCA. 3. Lastly, this data frame is used as input in a Principal Component Analysis.
It is exactly equivalent to MCA with one orthogonal instrumental variable (see MCAoiv)
Returns an object of class stMCA. This object will be similar to resmca argument, still it does not comprehend modified rates, categories contributions and variables contributions.
Nicolas Robette
Bry X., Robette N., Roueff O., 2016, « A dialogue of the deaf in the statistical theater? Adressing structural effects within a geometric data analysis framework », Quality & Quantity, 50(3), pp 1009–1020 [https://link.springer.com/article/10.1007/s11135-015-0187-z]
# standardized MCA of Music example data set # controlling for age ## and then draws the cloud of categories. data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) stmca <- stMCA(mca, control = list(Music$Age))# standardized MCA of Music example data set # controlling for age ## and then draws the cloud of categories. data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) stmca <- stMCA(mca, control = list(Music$Age))
From MCA results, computes statistics (coordinates, squared cosines) for supplementary individuals.
supind(resmca, supdata) indsup(resmca, supdata)supind(resmca, supdata) indsup(resmca, supdata)
resmca |
object of class |
supdata |
data frame with the supplementary individuals. It must have the same factors as the data frame used as input for the initial MCA. |
Returns a list with the following items :
coord |
matrix of individuals coordinates |
cos2 |
matrix of individuals squared cosines |
indsup is softly deprecated. Please use supind instead.
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
ggadd_supind,textindsup, supvar, supvars
# specific MCA of Music example data set # excluding the first two observations data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[3:nrow(Music),1:5], excl = junk) # computes coordinates and squared cosines # of the first two (supplementary) observations supind(mca,Music[1:2,1:5])# specific MCA of Music example data set # excluding the first two observations data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[3:nrow(Music),1:5], excl = junk) # computes coordinates and squared cosines # of the first two (supplementary) observations supind(mca,Music[1:2,1:5])
From MCA results, computes statistics (weights, coordinates, contributions, test-values, variances) for a categorical supplementary variable.
supvar(resmca, var) varsup(resmca, var)supvar(resmca, var) varsup(resmca, var)
resmca |
object of class |
var |
the categorical supplementary variable. It does not need to have been used at the MCA step. |
Returns a list:
weight |
numeric vector of categories weights |
coord |
data frame of categories coordinates |
cos2 |
data frame of categories squared cosines |
var |
data frame of categories within variances, variance between and within categories and variable squared correlation ratio (eta2) |
typic |
data frame of categories typicality test statistics |
pval |
data frame of categories p-values from typicality test statistics |
cor |
data frame of categories correlation coefficients |
varsup is softly deprecated. Please use supvar instead.
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
supvars, ggadd_supvar, ggadd_supvars, textvarsup, supind
# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # computes statistics for Age supplementary variable supvar(mca,Music$Age)# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # computes statistics for Age supplementary variable supvar(mca,Music$Age)
From MCA results, computes statistics (weights, coordinates, squared cosines, contributions, test-values, variances) for categorical supplementary variables.
supvars(resmca, vars) varsups(resmca, vars)supvars(resmca, vars) varsups(resmca, vars)
resmca |
object of class |
vars |
A data frame of categorical supplementary variables. All these variables should be factors. |
Returns a list with the following items :
weight |
numeric vector of categories weights |
coord |
data frame of categories coordinates |
cos2 |
data frame of categories squared cosines |
var |
a list of data frames of categories within variances, variance between and within categories and variable square correlation ratio (eta2) |
typic |
data frame of categories typicality test statistics |
pval |
data frame of categories p-values from typicality test statistics |
cor |
data frame of categories correlation coefficients |
varsups is softly deprecated. Please use supvars instead.
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
supvar, ggadd_supvar, ggadd_supvars, textvarsup, supind
# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # computes statistics for Gender and Age supplementary variables supvars(mca, Music[, c("Gender","Age")])# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # computes statistics for Gender and Age supplementary variables supvars(mca, Music[, c("Gender","Age")])
Identifies the categories that contribute the most to a given dimension of a Multiple Correspondence Analysis and organizes these informations into a fancy table.
tabcontrib(resmca, dim = 1, best = TRUE, dec = 2, shortlabs = FALSE)tabcontrib(resmca, dim = 1, best = TRUE, dec = 2, shortlabs = FALSE)
resmca |
object of class |
dim |
dimension to describe (default is 1st dimension) |
best |
if FALSE, displays all the categories; if TRUE (default), displays only categories with contributions higher than average |
dec |
integer. The number of decimals for the results (default is 2) |
shortlabs |
logical. If TRUE, the data frame will have short column names, so that all columns can be displayed side by side on a laptop screen. Default is FALSE (long explicit column names). |
A data frame with the following contributions.:
Variable |
names of the variables |
Category |
names of the categories |
Weight |
weights of the categories |
Quality of representation |
quality of representation (squared cosine) of the categories on the axis |
Contribution (left) |
contributions of the categories located on one side of the axis |
Contribution (right) |
contributions of the categories located on the other side of the axis |
Total contribution |
contributions summed by variable |
Cumulated contribution |
cumulated sum of the contributions |
Contribution of deviation |
for each variable, contribution of the deviation between the barycenter of the categories located on one side of the axis and the barycenter of those located on the other side |
Proportion to variable |
contribution of deviation expressed as a proportion of the contribution of the variable |
Nicolas Robette
Le Roux B. and Rouanet H., Multiple Correspondence Analysis, SAGE, Series: Quantitative Applications in the Social Sciences, Volume 163, CA:Thousand Oaks (2010).
Le Roux B. and Rouanet H., Geometric Data Analysis: From Correspondence Analysis to Stuctured Data Analysis, Kluwer Academic Publishers, Dordrecht (June 2004).
dimcontrib, dimdescr, dimeta2, dimtypicality
# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # main contributions on axis 1 tabcontrib(mca, 1) # main contributions on axis 2 tabcontrib(mca, 2)# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # main contributions on axis 1 tabcontrib(mca, 1) # main contributions on axis 2 tabcontrib(mca, 2)
The data concerns tastes for music and movies of a set of 2000 individuals. It contains 5 variables of likes for music genres (french pop, rap, rock, jazz and classical), 6 variables of likes for movie genres (comedy, crime, animation, science fiction, love, musical) and 2 additional variables (gender and age).
data(Taste)data(Taste)
A data frame with 2000 observations and the following 13 variables:
FrenchPopfactor with levels No, Yes, NA
Rapfactor with levels No, Yes, NA
Rockfactor with levels No, Yes, NA
Jazzfactor with levels No, Yes, NA
Classicalfactor with levels No, Yes, NA
Comedyfactor with levels No, Yes, NA
Crimefactor with levels No, Yes, NA
Animationfactor with levels No, Yes, NA
SciFifactor with levels No, Yes, NA
Lovefactor with levels No, Yes, NA
Musicalfactor with levels No, Yes, NA
Genderfactor with levels Men, Women
Agefactor with levels 15-24, 25-49, 50+
Educfactor with levels none, low, medium, high
NA stands for "not available"
data(Taste) str(Taste)data(Taste) str(Taste)
Adds supplementary individuals to a MCA cloud of the individuals.
textindsup(resmca, supdata, axes = c(1, 2), col = "darkred")textindsup(resmca, supdata, axes = c(1, 2), col = "darkred")
resmca |
object of class |
supdata |
data frame with the supplementary individuals. It must have the same factors as the data frame used as input for the initial MCA. |
axes |
numeric vector of length 2, specifying the dimensions (axes) to plot (default is c(1,2)) |
col |
color for the labels of the categories (default is "darkred") |
Nicolas Robette
supind, plot.speMCA, plot.csMCA
# specific MCA of Music example data set # excluding the first two observations data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[3:nrow(Music), 1:5], excl = junk) # cloud of active individuals # with the two supplementary individuals plot(mca, type = "i") textindsup(mca, Music[1:2, 1:5])# specific MCA of Music example data set # excluding the first two observations data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[3:nrow(Music), 1:5], excl = junk) # cloud of active individuals # with the two supplementary individuals plot(mca, type = "i") textindsup(mca, Music[1:2, 1:5])
Adds a categorical supplementary variable to a MCA cloud of categories.
textvarsup(resmca, var, sel = 1:nlevels(var), axes = c(1, 2), col = "black", app = 0, vname = NULL)textvarsup(resmca, var, sel = 1:nlevels(var), axes = c(1, 2), col = "black", app = 0, vname = NULL)
resmca |
object of class |
var |
the categorical supplementary variable. It does not need to have been used at the MCA step. |
sel |
numeric vector of indexes of the categories of the supplementary variable to be added to the plot (by default, labels are plotted for every categories) |
axes |
numeric vector of length 2, specifying the dimensions (axes) to plot (default is c(1,2)) |
col |
color for the labels of the categories (default is black) |
app |
numerical value. If 0 (default), only the labels are plotted and their size is constant; if 1, only the labels are plotted and their size is proportional to the weights of the categories; if 2, points (triangles) and labels are plotted, and points size is proportional to the weight of the categories. |
vname |
a character string to be used as a prefix for the labels of the categories (null by default) |
Nicolas Robette
supvar, supvars, plot.speMCA, plot.csMCA
# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # cloud of categories # with Gender and Age supplementary variables plot(mca, col = "gray") textvarsup(mca, Music$Gender,col = "darkred") textvarsup(mca, Music$Age, sel = c(1,3), col = "orange", vname = "age", app = 1)# specific MCA of Music example data set data(Music) junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA") mca <- speMCA(Music[,1:5], excl = junk) # cloud of categories # with Gender and Age supplementary variables plot(mca, col = "gray") textvarsup(mca, Music$Gender,col = "darkred") textvarsup(mca, Music$Age, sel = c(1,3), col = "orange", vname = "age", app = 1)
This function has been moved to the translate.logit package.
translate.logit(...)translate.logit(...)
... |
arguments are ignored |
Within-class MCA, also called conditional MCA
wcMCA(data, class, excl = NULL, row.w = NULL, ncp = 5)wcMCA(data, class, excl = NULL, row.w = NULL, ncp = 5)
data |
data frame with only categorical variables, i.e. factors |
class |
factor specifying the class |
excl |
numeric vector indicating the indexes of the "junk" categories (default is NULL). See |
row.w |
numeric vector of row weights. If NULL (default), a vector of 1 for uniform row weights is used. |
ncp |
number of dimensions kept in the results (by default 5) |
Within-class Multiple Correspondence Analysis is a MCA where the active categories are centered on the mean of their class (i.e. conditional frequencies) instead of the overall mean (i.e. marginal frequencies).
It is also known as "conditional MCA" and can be seen as a special case of MCA on orthogonal instrumental variables, with only one (categorical) instrumental variable.
An object of class speMCA, with an additional item :
ratio |
the within-class inertia percentage |
.
The code is adapted from speMCA function.
As in speMCA, if there are NAs in data, these NAs will be automatically considered as junk categories. If one desires more flexibility, data should be recoded to add explicit factor levels for NAs and then excl option may be used to select the junk categories.
Nicolas Robette
Escofier B., 1990, Analyse des correspondances multiples conditionnelle, La revue de Modulad, 5, 13-28.
Lebart L., Morineau A. et Warwick K., 1984, Multivariate Descriptive Statistical Analysis, John Wiley and sons, New-York.)
# within-class analysis of tea data # with SPC as class library(FactoMineR) data(tea) res <- wcMCA(tea[,1:18], tea$SPC) res$ratio ggcloud_variables(res)# within-class analysis of tea data # with SPC as class library(FactoMineR) data(tea) res <- wcMCA(tea[,1:18], tea$SPC) res$ratio ggcloud_variables(res)
Within-class Principal Component Analysis
wcPCA(X, class, scale.unit = TRUE, ncp = 5, ind.sup = NULL, quanti.sup = NULL, quali.sup = NULL, row.w = NULL, col.w = NULL, graph = FALSE, axes = c(1, 2))wcPCA(X, class, scale.unit = TRUE, ncp = 5, ind.sup = NULL, quanti.sup = NULL, quali.sup = NULL, row.w = NULL, col.w = NULL, graph = FALSE, axes = c(1, 2))
X |
a data frame with n rows (individuals) and p columns (numeric variables) |
class |
factor specifying the class |
scale.unit |
a boolean, if TRUE (default) then data are scaled to unit variance |
ncp |
number of dimensions kept in the results (by default 5) |
ind.sup |
a vector indicating the indexes of the supplementary individuals |
quanti.sup |
a vector indicating the indexes of the quantitative supplementary variables |
quali.sup |
a vector indicating the indexes of the categorical supplementary variables |
row.w |
an optional row weights (by default, a vector of 1 for uniform row weights); the weights are given only for the active individuals |
col.w |
an optional column weights (by default, uniform column weights); the weights are given only for the active variables |
graph |
boolean, if TRUE a graph is displayed. Default is FALSE. |
axes |
a length 2 vector specifying the components to plot |
Within-class Principal Component Analysis is a PCA where the active variables are centered on the mean of their class instead of the overall mean.
It is a "conditional" PCA and can be seen as a special case of PCA with orthogonal instrumental variables, with only one (categorical) instrumental variable.
An object of class PCA from FactoMineR package, with an additional item :
ratio |
the within-class inertia percentage |
.
The code is adapted from PCA function from FactoMineR package.
Nicolas Robette
Escofier B., 1990, Analyse des correspondances multiples conditionnelle, La revue de Modulad, 5, 13-28.
Lebart L., Morineau A. et Warwick K., 1984, Multivariate Descriptive Statistical Analysis, John Wiley and sons, New-York.)
# within-class analysis of decathlon data # with quatiles of points as class library(FactoMineR) data(decathlon) points <- cut(decathlon$Points, c(7300, 7800, 8000, 8120, 8900), c("Q1","Q2","Q3","Q4")) res <- wcPCA(decathlon[,1:10], points) plot(res, choix = "var")# within-class analysis of decathlon data # with quatiles of points as class library(FactoMineR) data(decathlon) points <- cut(decathlon$Points, c(7300, 7800, 8000, 8120, 8900), c("Q1","Q2","Q3","Q4")) res <- wcPCA(decathlon[,1:10], points) plot(res, choix = "var")
These functions have been moved to the descriptio package. You may check its documentation here :
https://nicolas-robette.github.io/descriptio/
wtable(...) pem(...) phi.table(...) assoc.twocont(...) assoc.twocat(...) assoc.catcont(...) assoc.yx(...) darma(...) catdesc(...) condesc(...) ggassoc_phiplot(...) ggassoc_boxplot(...) ggassoc_scatter(...) ggassoc_crosstab(...)wtable(...) pem(...) phi.table(...) assoc.twocont(...) assoc.twocat(...) assoc.catcont(...) assoc.yx(...) darma(...) catdesc(...) condesc(...) ggassoc_phiplot(...) ggassoc_boxplot(...) ggassoc_scatter(...) ggassoc_crosstab(...)
... |
arguments are ignored |