Discriminant Analysis

Description

Descriptive discriminant analysis, aka "Analyse Factorielle Discriminante" for the French school of multivariate data analysis.

Usage

DA(data, class, row.w = NULL, type = "FR")

Arguments

Details

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".

Value

An object of class PCA from FactoMineR package, with class as qualitative supplementary variable, and one additional item :

Note

The code is adapted from a script from Marie Chavent. See: https://marie-chavent.perso.math.cnrs.fr/teaching/

Author(s)

Marie Chavent, Nicolas Robette

References

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.

See Also

bcPCA, PCAiv

Examples

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")

Discriminant Analysis of Qualitative Variables

Description

Descriptive discriminant analysis (aka "Analyse Factorielle Discriminante" for the French school of multivariate data analysis) with qualitative variables.

Usage

DAQ(data, class, excl = NULL, row.w = NULL,
    type = "FR", select = TRUE)

Arguments

Details

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".

Value

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 :

Note

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.

Author(s)

Nicolas Robette

References

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.

See Also

DA, bcMCA, MCAiv, speMCA

Examples

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")

Multiple Correspondence Analysis with Instrumental Variables

Description

Multiple Correspondence Analysis with Instrumental Variables

Usage

MCAiv(Y, X, excl = NULL, row.w = NULL, ncp = 5)

Arguments

Details

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".

Value

An object of class PCA from FactoMineR package, with Y and X as supplementary variables, and an additional item :

.

Note

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.

Author(s)

Nicolas Robette

References

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.)

See Also

bcMCA, DAQ, bcPCA, DA, PCAiv

Examples

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

Description

Multiple Correspondence Analysis with Orthogonal Instrumental Variables

Usage

MCAoiv(X, Z, excl = NULL, row.w = NULL, ncp = 5)

Arguments

Details

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.

Value

An object of class PCA from FactoMineR package, with X as supplementary variables, and an additional item :

.

Note

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.

Author(s)

Nicolas Robette

References

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.)

See Also

wcMCA, wcPCA, PCAoiv

Examples

library(FactoMineR)
data(tea)
mcaoiv <- MCAoiv(tea[,1:18], tea[,19:22])
mcaoiv$ratio
plot(mcaoiv, choix = "ind", invisible = "ind", col.quali = "black")

Music (data)

Description

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).

Usage

data(Music)

Format

A data frame with 500 observations and the following 7 variables:

FrenchPop

factor with levels No, Yes, NA

Rap

factor with levels No, Yes, NA

Rock

factor with levels No, Yes, NA

Jazz

factor with levels No, Yes, NA

Classical

factor with levels No, Yes, NA

Gender

factor with levels Men, Women

Age

factor with levels 15-24, 25-49, 50+

OnlyMus

factor with levels Daily, Often, Rare, Never, indicating how often one only listens to music.

Daily

is a factor with levels No, Yes indicating if one listens to music every day.

Details

NA stands for "not available"

Examples

data(Music)
str(Music)

Principal Component Analysis with Instrumental Variables

Description

Principal Component Analysis with Instrumental Variables

Usage

PCAiv(Y, X, row.w = NULL, ncp = 5)

Arguments

Details

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"

Value

An object of class PCA from FactoMineR package, with X as supplementary variables, and an additional item :

.

Author(s)

Nicolas Robette

References

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.)

See Also

bcPCA, DA, bcMCA, DAQ, MCAiv

Examples

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

Description

Principal Component Analysis with Orthogonal Instrumental Variables

Usage

PCAoiv(X, Z, row.w = NULL, ncp = 5)

Arguments

Details

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.

Value

An object of class PCA from FactoMineR package, and an additional item :

.

Author(s)

Nicolas Robette

References

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.)

See Also

wcPCA, wcMCA, MCAoiv

Examples

library(FactoMineR)
data(decathlon)
pcaoiv <- PCAoiv(decathlon[,1:10], decathlon[,12:13])
plot(pcaoiv, choix = "var", invisible = "quanti.sup")

Taste (data)

Description

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).

Usage

data(Taste)

Format

A data frame with 2000 observations and the following 13 variables:

FrenchPop

factor with levels No, Yes, NA

Rap

factor with levels No, Yes, NA

Rock

factor with levels No, Yes, NA

Jazz

factor with levels No, Yes, NA

Classical

factor with levels No, Yes, NA

Comedy

factor with levels No, Yes, NA

Crime

factor with levels No, Yes, NA

Animation

factor with levels No, Yes, NA

SciFi

factor with levels No, Yes, NA

Love

factor with levels No, Yes, NA

Musical

factor with levels No, Yes, NA

Gender

factor with levels Men, Women

Age

factor with levels 15-24, 25-49, 50+

Educ

factor with levels none, low, medium, high

Details

NA stands for "not available"

Examples

data(Taste)
str(Taste)

Plots for Ascending Hierarchical Clustering

Description

Draws various plots for Ascending Hierarchical Clustering results.

Usage

ahc.plots(ahc, distance = NULL, max.cl = 20, type = "dist")

Arguments

Details

The three kinds of plots proposed with this function are aimed at guiding in the choice of the number of clusters.

Author(s)

Nicolas Robette

See Also

dist.chi2

Examples

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")

Cosine similarities and angles between CSA and MCA

Description

Computes the cosines similarities and angles between the components of a CSA and those of a MCA.

Usage

angles.csa(rescsa, resmca)

Arguments

Value

A list of matrices:

Note

This function is adapted from csa.measures in sco.ca package.

Author(s)

Nicolas Robette

References

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).

See Also

MCA, speMCA, csMCA

Examples

## 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)

Bar plot of contributions

Description

From MCA results, plots contributions to the axes.

Usage

barplot_contrib(resmca, dim = 1, which = "var",
  sort = FALSE, col = "tomato4", repel = FALSE)
  

Arguments

Details

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.

Value

a ggplot2 object

Author(s)

Nicolas Robette

References

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).

See Also

speMCA, tabcontrib

Examples

# 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

Description

Between-class MCA, also called Barycentric Discriminant Analysis

Usage

bcMCA(data, class, excl = NULL, row.w = NULL)

Arguments

Details

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.

Value

An object of class CA from FactoMineR package, with the indicator matrix of data as supplementary rows, and an additional item :

Author(s)

Nicolas Robette

References

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.)

See Also

DAQ, MCAiv

Examples

library(FactoMineR)
data(tea)
res <- bcMCA(tea[,1:18], tea$SPC)
# categories of class
plot(res, invisible = c("col", "row.sup"))
# Variables in tea data
plot(res, invisible = c("row", "row.sup"))
# between-class inertia percentage
res$ratio

Between-class Principal Component Analysis

Description

Between-class Principal Component Analysis

Usage

bcPCA(data, class, row.w = NULL, scale.unit = TRUE, ncp = 5)

Arguments

Details

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.

Value

An object of class PCA from FactoMineR package, with the original data as supplementary individuals, and an additional item :

Author(s)

Nicolas Robette

References

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.)

See Also

PCAiv, DA

Examples

library(FactoMineR)
data(decathlon)
points <- cut(decathlon$Points, c(7300, 7800, 8000, 8120, 8900), c("Q1","Q2","Q3","Q4"))
res <- bcPCA(decathlon[,1:10], points)
# categories of class
plot(res, choix = "ind", invisible = "ind.sup")
# variables in decathlon data
plot(res, choix = "var")
# between-class inertia percentage
res$ratio

Bootstrap validation (supplementary variables)

Description

Bootstrap validation of MCA, through the computation of the coordinates of supplementary variables for bootstrap replications of the data.

Usage

bootvalid_supvars(resmca, vars = NULL, axes = c(1,2), K = 30)

Arguments

Details

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).

Value

A data frame with the following elements :

Author(s)

Nicolas Robette

References

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.

See Also

ggbootvalid_supvars, bootvalid_variables

Examples

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 (active variables)

Description

Bootstrap validation of MCA, through the computation of the coordinates of active variables for bootstrap replications of the data.

Usage

bootvalid_variables(resmca, axes = c(1,2), type = "partial", K = 30)

Arguments

Details

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.

Value

A data frame with the following elements :

Author(s)

Nicolas Robette

References

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.

See Also

ggbootvalid_variables, bootvalid_supvars

Examples

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)

Additive Breakdowns of Variances

Description

Computes three additive breakdown of variances for the interaction between two supplementary variables

Usage

break_interaction(resmca, v1, v2)

Arguments

Details

This function reproduces the approach developed in Le Roux & Rouanet (2010) in section 4.4, in particular table 4.5.

Value

A data frame

Author(s)

Nicolas Robette

References

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).

See Also

ggadd_interaction, ggadd_partial

Examples

# 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)
# breakdowns of variance 
# for the interaction between Gender and Age
break_interaction(mca, Taste$Gender, Taste$Age)

Burt table

Description

Computes a Burt table from a data frame composed of categorical variables.

Usage

burt(data)

Arguments

Details

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.

Value

Returns a square matrix. Its dimension is equal to the total number of categories in the data frame.

Author(s)

Nicolas Robette

References

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).

See Also

dichotom

Examples

## 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

Description

Coinertia analysis between two groups of categorical variables

Usage

coiMCA(Xa, Xb, 
       excl.a = NULL, excl.b = NULL,
       row.w = NULL, ncp = 5)

Arguments

Details

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

Value

An object of class CA from FactoMineR package, with an additional item :

Author(s)

Nicolas Robette

References

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.

See Also

coiPCA, rvcoef

Examples

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$RV

Coinertia analysis between two groups of numerical variables

Description

Coinertia analysis between two groups of numerical variables

Usage

coiPCA(Xa, Xb, row.w = NULL, ncp = 5)

Arguments

Details

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

Value

An object of class PCA from FactoMineR package, with an additional item :

Author(s)

Nicolas Robette

References

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.

See Also

coiMCA, rvcoef

Examples

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$RV

Concentration ellipses

Description

Adds concentration ellipses or other kinds of inertia ellipses to the cloud of individuals of a MCA.

Usage

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)

Arguments

Details

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.

Author(s)

Nicolas Robette

References

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).

See Also

plot.speMCA, plot.csMCA, plot.multiMCA, plot.stMCA

Examples

## 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")

Contributions of active variables

Description

From MCA results, computes contributions of categories and variables to the axes and the overall cloud.

Usage

contrib(resmca)

Arguments

Details

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).

Value

A list of data frames:

Author(s)

Nicolas Robette

References

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).

See Also

speMCA, supvar, tabcontrib

Examples

# 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)

Class Specific Analysis

Description

Performs a "class specific"" Multiple Correspondence Analysis, i.e. a variant of MCA consisting in analyzing a subcloud of individuals.

Usage

csMCA(data, subcloud = rep(TRUE, times = nrow(data)), excl = NULL, ncp = 5, 
row.w = rep(1, times = nrow(data)))

Arguments

Details

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).

Value

An object of class csMCA, i.e. a list including:

Author(s)

Nicolas Robette

References

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).

See Also

ijunk, speMCA

Examples

# 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)

Dichotomizes the variables in a data frame

Description

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)

Usage

dichotom(data, out = "numeric")

Arguments

Value

Returns a data frame with dichotomized variables. The number of columns is equal to the total number of categories in the input data.

Author(s)

Nicolas Robette, Julien Barnier

Examples

## 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 mixed format data frame

Description

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.

Usage

dichotomixed(data, out = "numeric")

Arguments

Value

Returns a data frame with numerical variables and dichotomized factor variables

Author(s)

Nicolas Robette

Examples

## 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)

Description of the contributions to axes

Description

Identifies the categories and individuals that contribute the most to each dimension obtained by a Multiple Correspondence Analysis.

Usage

dimcontrib(resmca, dim = c(1,2), best = TRUE)

Arguments

Details

Contributions are sorted and assigned a positive or negative sign according to the corresponding categories or individuals coordinates, so as to facilitate interpretation.

Value

Returns a list with the following items :

Note

Contributions of individuals cannot be computed for objects created by wcMCA function.

Author(s)

Nicolas Robette

References

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).

See Also

tabcontrib, dimdescr, dimeta2, dimtypicality

Examples

# 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)

Description of the dimensions

Description

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.

Usage

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)

Arguments

Details

See condesc.

Value

Returns a list of ncp lists including:

Author(s)

Nicolas Robette

References

Husson, F., Le, S. and Pages, J. (2010). Exploratory Multivariate Analysis by Example Using R, Chapman and Hall.

See Also

condesc, dimcontrib, dimeta2, dimtypicality

Examples

# 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)

Correlation ratios (aka eta-squared) of supplementary variables

Description

Computes correlation ratios (also known as eta-squared) for a list of supplementary variables of a MCA.

Usage

dimeta2(resmca, vars, dim = c(1,2))

Arguments

Value

Returns a data frame with supplementary variables as rows and MCA axes as columns.

Author(s)

Nicolas Robette

References

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).

See Also

dimdescr, dimcontrib, dimtypicality

Examples

# 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")])

Typicality tests for supplementary variables

Description

Computes typicality tests for a list of supplementary variables of a MCA.

Usage

dimtypicality(resmca, vars, dim = c(1,2), max.pval = 1)

Arguments

Value

Returns a list of data frames giving the typicality test statistics and p-values of the supplementary categories for the different axes.

Author(s)

Nicolas Robette

References

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).

See Also

dimdescr, dimeta2, dimcontrib

Examples

# 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")])

Chi-squared distance

Description

Computes the chi-squared distance between the rows of a data frame of factors.

Usage

dist.chi2(X)

Arguments

Details

This function is adapted from chi2Dist function in ExPosition package.

Value

A symmetrical matrix of distances

Author(s)

Nicolas Robette

Examples

data(Music)
d <- dist.chi2(Music[,1:5])
# a short piece of the distance matrix
d[1:3, 1:3]

Flips the coordinates

Description

Flips the coordinates of the individuals and the categories on one or more dimensions of a MCA.

Usage

flip.mca(resmca, dim = 1)

Arguments

Value

Returns an object of the same class as resmca

Author(s)

Nicolas Robette

References

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).

See Also

ggcloud_variables, ggcloud_indiv

Examples

# 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")

Generalized Principal Component Analysis

Description

Generalized Principal Component Analysis

Usage

gPCA(X, row.w = NULL, col.w = NULL, center = FALSE, scale = FALSE, tol = 1e-07)

Arguments

Details

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".

Value

An object of class PCA from FactoMineR package

Author(s)

Nicolas Robette

References

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.

Examples

library(FactoMineR)
data(decathlon)
res <- gPCA(decathlon[,1:10], center = TRUE, scale = TRUE)
plot(res, choix = "var")

Names of the categories in a data frame

Description

Returns a vector of names corresponding the the categories in a data frame exclusively composed of categorical variables.

Usage

getindexcat(data)

Arguments

Details

This function may be useful prior to a specific MCA, to identify the indexes of the 'junk' categories to exclude.

Value

Returns a character vector with the names of the categories of the variables in the data frame

Author(s)

Nicolas Robette

See Also

ijunk, speMCA, csMCA

Examples

data(Music)
getindexcat(Music[,1:5])
mca <- speMCA(Music[,1:5], excl = c(3,6,9,12,15))

Plot of attractions between categories

Description

Adds attractions between categories, as measured by phi coefficients or percentages of maximum deviation (PEM), by plotting segments onto a MCA cloud of variables.

Usage

ggadd_attractions(p, resmca, axes = c(1,2), measure = "phi", min.asso = 0.3,
col.segment = "lightgray", col.text = "black", text.size = 3)

Arguments

Value

a ggplot2 object

Author(s)

Nicolas Robette

References

Cibois, Philippe. Les méthodes d’analyse d’enquêtes. Nouvelle édition [en ligne]. Lyon: ENS Éditions, 2014. <http://books.openedition.org/enseditions/1443>

See Also

ggcloud_variables

Examples

# 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)

Convex hulls for a categorical supplementary variable

Description

Adds convex hulls for a categorical variable to a MCA cloud of individuals.

Usage

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")

Arguments

Value

a ggplot2 object

Note

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().

Author(s)

Nicolas Robette

References

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).

See Also

ggcloud_indiv, ggadd_supvar, ggadd_supvars, ggadd_kellipses, ggadd_ellipses, ggadd_interaction, ggsmoothed_supvar, ggadd_corr, ggadd_density

Examples

# 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)

Heatmap of under/over-representation of a supplementary variable

Description

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.

Usage

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")

Arguments

Details

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.

Value

a ggplot2 object

Author(s)

Nicolas Robette

References

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).

See Also

ggcloud_variables, ggadd_supvar, ggadd_supvars, ggadd_kellipses, ggadd_ellipses, ggadd_interaction, ggsmoothed_supvar, ggadd_chulls, ggadd_density

Examples

# 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)

Density plot of a supplementary variable

Description

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.

Usage

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)

Arguments

Value

a ggplot2 object

Author(s)

Nicolas Robette

References

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).

See Also

ggcloud_indiv, ggadd_supvar, ggadd_supvars, ggadd_kellipses, ggadd_ellipses, ggadd_interaction, ggsmoothed_supvar, ggadd_chulls, ggadd_corr

Examples

# 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")

Confidence ellipses

Description

Adds confidence ellipses for a categorical variable to a MCA cloud of individuals

Usage

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")

Arguments

Details

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.

Value

a ggplot2 object

Note

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().

Author(s)

Nicolas Robette

References

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).

See Also

ggcloud_indiv, ggadd_supvar, ggadd_supvars, ggadd_kellipses, ggadd_density, ggadd_interaction, ggsmoothed_supvar, ggadd_chulls, ggadd_corr

Examples

# 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)

Plot of interactions between two categorical supplementary variables

Description

Adds the interactions between two categorical supplementary variables to a MCA cloud of variables

Usage

ggadd_interaction(p, resmca, v1, v2, sel1 = 1:nlevels(v1), sel2 = 1:nlevels(v2),
axes = c(1,2), cloud = "v", textsize = 5, lines = TRUE, dashes = TRUE, 
legend = "none", force = 1, max.overlaps = Inf)

Arguments

Value

a ggplot2 object

Note

Lines and labels are colored according to the first 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().

Author(s)

Nicolas Robette

References

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).

See Also

ggcloud_variables, ggadd_supvar, ggadd_supvars, ggadd_kellipses, ggadd_ellipses, ggadd_corr, ggsmoothed_supvar, ggadd_chulls, ggadd_density

Examples

# 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)

Concentration ellipses and k-inertia ellipses

Description

Adds concentration ellipses and other kinds of k-inertia ellipses for a categorical variable to a MCA cloud of individuals.

Usage

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")

Arguments

Details

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.

Value

a ggplot2 object

Note

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().

Author(s)

Nicolas Robette

References

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).

See Also

ggcloud_indiv, ggadd_supvar, ggadd_supvars, ggadd_ellipses, ggadd_density, ggadd_interaction, ggsmoothed_supvar, ggadd_chulls, ggadd_corr

Examples

# 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)

Main and partial effect of a supplementary variable

Description

Adds the main and partial effects of a supplementary variable to a MCA cloud of individuals, with one or more supplementary partialled out

Usage

ggadd_partial(p, resmca, var, controls, excl = NULL,
axes = c(1,2), col = "black", textsize = 4, lines = TRUE, dashes = TRUE, 
legend = "right", force = 1, max.overlaps = Inf)

Arguments

Value

a ggplot2 object

Note

The partial effects of the supplementary variable are computed with the Average Marginal Effects of a linear regression, with individual coordinates as dependent variable, and the supplementary and control variables as independent variables.

Author(s)

Nicolas Robette

References

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).

See Also

ggcloud_variables, ggadd_supvar, ggadd_supvars, ggadd_interaction

Examples

# 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)
# effect of education,
# with age partialled out (partial effect) or not (main effect)
p <- ggcloud_indiv(mca, col = "grey95")
ggadd_partial(p, mca, Taste$Educ, Taste$Age)

Plot of supplementary individuals

Description

Adds supplementary individuals to a MCA cloud of the individuals

Usage

ggadd_supind(p, resmca, dfsup, axes = c(1,2), 
col = "black", textsize = 5, pointsize = 2)

Arguments

Details

The function uses the row names of dfsup as labels for the individuals.

Author(s)

Nicolas Robette

See Also

supind, ggcloud_indiv

Examples

# 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])

Plot of a categorical supplementary variable

Description

Adds a categorical supplementary variable to a MCA cloud of variables.

Usage

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)

Arguments

Value

a ggplot2 object

Author(s)

Nicolas Robette

References

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).

See Also

ggcloud_variables, ggadd_supvars, ggadd_ellipses, ggadd_kellipses, ggadd_density, ggadd_interaction, ggsmoothed_supvar, ggadd_chulls, ggadd_corr

Examples

# 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)

Plot of categorical supplementary variables

Description

Adds categorical supplementary variables to a MCA cloud of variables.

Usage

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)

Arguments

Value

a ggplot2 object

Note

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().

Author(s)

Nicolas Robette

References

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).

See Also

ggcloud_variables, ggadd_supvar, ggadd_ellipses, ggadd_kellipses, ggadd_density, ggadd_interaction, ggsmoothed_supvar, ggadd_chulls, ggadd_corr

Examples

# 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)

Plot of variables on a single axis

Description

Plots variables on a single axis of a Multiple Correspondence Analysis. Variables can be active or supplementary.

Usage

ggaxis_variables(resmca, var = NULL, axis = 1, 
min.ctr = NULL, prop = NULL,
underline = FALSE, col = NULL, vlab = TRUE,
force = 1, max.overlaps = Inf)

Arguments

Value

a ggplot2 object

Author(s)

Nicolas Robette

References

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).

See Also

ggcloud_variables

Examples

# 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 of bootstrap validation (supplementary variables)

Description

Ellipses for bootstrap validation of MCA, through the computation of the coordinates of supplementary variables for bootstrap replications of the data.

Usage

ggbootvalid_supvars(resmca, vars = NULL, axes = c(1,2), K = 30,
                    ellipse = "norm", level = 0.95,
                    col = NULL, active = FALSE, legend = "right")

Arguments

Details

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.

Value

a ggplot2 object

Note

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().

Author(s)

Nicolas Robette

References

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.

See Also

bootvalid_supvars, ggbootvalid_variables

Examples

# 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 of bootstrap validation (active variables)

Description

Ellipses for bootstrap validation of MCA, through the computation of the coordinates of active variables for bootstrap replications of the data.

Usage

ggbootvalid_variables(resmca, axes = c(1,2), type = "partial", K = 30,
                      ellipse = "norm", level = 0.95,
                      col = NULL, legend = "right")

Arguments

Details

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.

Value

a ggplot2 object

Note

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().

Author(s)

Nicolas Robette

References

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.

See Also

bootvalid_variables , ggbootvalid_supvars

Examples

# 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)

Plot of the cloud of individuals

Description

Plots a Multiple Correspondence Analysis cloud of individuals.

Usage

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")

Arguments

Details

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.

Value

a ggplot2 object

Note

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().

Author(s)

Anton Perdoncin, Nicolas Robette

References

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).

See Also

ggcloud_variables

Examples

# 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)

Plot of the cloud of variables

Description

Plots a Multiple Correspondence Analysis cloud of variables.

Usage

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)

Arguments

Value

a ggplot2 object

Note

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.

Author(s)

Anton Perdoncin, Nicolas Robette

References

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).

See Also

ggcloud_indiv

Examples

# 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")

eta-squared plot

Description

Plots the eta-squared (squared correlation ratios) of the active variables of a MCA.

Usage

ggeta2_variables(resmca, axes = c(1,2))

Arguments

Details

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.

Value

a ggplot2 object

Author(s)

Nicolas Robette

References

Escofier B. and Pagès J., 2008, Analyses factorielles simples et multiples, Dunod.

See Also

ggcloud_variables, ggadd_attractions

Examples

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 a supplementary variable

Description

Plots the density of a supplementary variable in a MCA space, using a grid, smoothing and interpolation (via inverse distance weighting.)

Usage

ggsmoothed_supvar(resmca, var, cat, axes = c(1,2), 
                  center = FALSE, scale = FALSE,
                  nc = c(20, 20), power = 2,
                  limits = NULL, pal = "RdBu")

Arguments

Details

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.

Value

a ggplot2 object

Author(s)

Nicolas Robette

References

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

See Also

ggadd_supvar, ggadd_supvars, ggadd_kellipses, ggadd_ellipses, ggadd_interaction, ggadd_corr, ggadd_chulls, ggadd_density

Examples

# 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)

Homogeneity test for a categorical supplementary variable

Description

From MCA results, computes a homogeneity test between categories of a supplementary variable, i.e. characterizes the homogeneity of several subclouds.

Usage

homog.test(resmca, var, dim = c(1,2))

Arguments

Value

Returns a list of lists, one for each selected dimension in the MCA. Each list has 2 elements :

Author(s)

Nicolas Robette

References

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).

See Also

supvar, supvars, dimtypicality

Examples

# 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)

App for junk categories of specific MCA

Description

This function launches a shiny app to define interactively the junk categories before a specific MCA.

Usage

ijunk(data, init_junk = NULL)

Arguments

Details

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.

Value

A character vector of junk categories

Author(s)

Nicolas Robette

See Also

speMCA, csMCA, getindexcat

Examples

## 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)

Medoids of clusters

Description

Computes the medoids of a cluster solution.

Usage

medoids(D, cl)

Arguments

Details

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).

Value

Returns a numeric vector with the indexes of medoids.

Author(s)

Nicolas Robette

References

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.

See Also

dist, hclust, cutree , pam

Examples

# 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)

Benzecri's modified rates of variance

Description

Computes Benzecri's modified rates of variance of a multiple correspondence analysis.

Usage

modif.rate(resmca)

Arguments

Details

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.

Value

Returns a list of two data frames. The first one is called raw and has 3 variables:

The second one is called modif and has 2 variables:

Author(s)

Nicolas Robette

References

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).

See Also

MCA, speMCA, csMCA

Examples

# MCA of Music' example data set
data(Music)
mca <- speMCA(Music[,1:5])
# modified rates of variance
modif.rate(mca)

Multiple Factor Analysis

Description

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.

Usage

multiMCA(l_mca, ncp = 5, compute.rv = FALSE)

Arguments

Details

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).

Value

Returns an object of class multiMCA, i.e. a list:

Author(s)

Nicolas Robette

References

Escofier, B. and Pages, J. (1994) "Multiple Factor Analysis (AFMULT package)". Computational Statistics and Data Analysis, 18, 121-140.

See Also

plot.multiMCA, speMCA, csMCA

Examples

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)

Nonsymmetric Correspondence Analysis

Description

Nonsymmetric correspondence analysis, for analysing contingency tables with a dependence structure

Usage

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)

Arguments

Details

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).

Value

An object of class CA from FactoMineR package, with an additional item :

Note

The code is adapted from the CA function in FactoMineR package.

Author(s)

Nicolas Robette

References

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.

See Also

nsca.biplot

Examples

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.tau

Biplot for Nonsymmetric Correspondence Analysis

Description

Biplot for Nonsymmetric correspondence analysis, for analysing contingency tables with a dependence structure

Usage

nsca.biplot(nsca, axes = c(1,2))

Arguments

Details

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).

Value

a ggplot2 object

Author(s)

Nicolas Robette

References

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.

See Also

nsCA

Examples

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.tau

Contributions to a plane

Description

For a given plane of a MCA, computes contributions and squared cosines of the active variables and categories and of the active individuals.

Usage

planecontrib(resmca, axes = c(1,2))

Arguments

Value

A list of two lists. The first deals with variables :

The second deals with observations :

Author(s)

Nicolas Robette

References

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).

See Also

dimcontrib, tabcontrib

Examples

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$var

Plot of class specific MCA

Description

Plots a class specific Multiple Correspondence Analysis (resulting from csMCA function), i.e. the clouds of individuals or categories.

Usage

## S3 method for class 'csMCA'
plot(x, type = "v", axes = 1:2, points = "all",
col = "dodgerblue4", app = 0, ...)

Arguments

Details

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.

Author(s)

Nicolas Robette

References

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).

See Also

csMCA, textvarsup, conc.ellipse

Examples

# 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)

Plot of Multiple Factor Analysis

Description

Plots Multiple Factor Analysis data, resulting from multiMCA function.

Usage

## 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, ...)

Arguments

Details

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).

Author(s)

Nicolas Robette

References

Escofier, B. and Pages, J. (1994) "Multiple Factor Analysis (AFMULT package)". Computational Statistics and Data Analysis, 18, 121-140.

See Also

multiMCA, textvarsup, speMCA, csMCA

Examples

# 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)

Plot of specific MCA

Description

Plots a specific Multiple Correspondence Analysis (resulting from speMCA function), i.e. the clouds of individuals or categories.

Usage

## S3 method for class 'speMCA'
plot(x, type = "v", axes = c(1,2), points = "all", col = "dodgerblue4", app = 0, ...)

Arguments

Details

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.

Author(s)

Nicolas Robette

References

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).

See Also

speMCA, textvarsup, conc.ellipse

Examples

# 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)

Plot of standardized MCA

Description

Plots a standardized Multiple Correspondence Analysis (resulting from stMCA function), i.e. the clouds of individuals or categories.

Usage

## S3 method for class 'stMCA'
plot(x, type = "v", axes = 1:2, points = "all", threshold = 2.58, groups=NULL, 
                            col = "dodgerblue4", app = 0, ...)

Arguments

Details

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).

Author(s)

Nicolas Robette

References

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]

See Also

stMCA, textvarsup, conc.ellipse

Examples

# 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)

Quadrant of active individuals

Description

Computes the quadrant of active individuals from a MCA.

Usage

quadrant(resmca, dim = c(1,2))

Arguments

Value

Returns a factor with four levels : upper_left, lower_left, upper_right, lower_right

Author(s)

Nicolas Robette

See Also

speMCA, csMCA

Examples

# 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)))

Quasi-correspondence analysis

Description

Transforms a symmetrical contingency table so that it can be used for quasi-correspondence analysis, also called correspondence analysis of incomplete contingency table.

Usage

quasindep(tab, order = 3, tol = 1e-6)

Arguments

Details

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).

Value

An object of the same class and dimensions as tab : the quasi-independence data to be analyzed with Correspondence Analysis.

Note

This function is adapted from Milan Bouchet-Valat's script in the supplementary material of his article indicated in the reference section.

References

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>

Examples

## 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)

Reshapes objects created with bcMCA()

Description

reshapes objects created with 'bcMCA()' so that they can be used with other functions from the package.

Usage

reshape_between(bcmca)

Arguments

Value

Returns an object of class bcMCA

Author(s)

Nicolas Robette

References

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.)

See Also

bcMCA

Examples

data(tea, package = "FactoMineR")
res <- bcMCA(tea[,1:18], tea$SPC)
res_ok <- reshape_between(res)
ggcloud_variables(res_ok)

RV coefficient

Description

Computes the RV coefficient between two groups of numerical variables.

Usage

rvcoef(Xa, Xb, row.w = NULL)

Arguments

Details

Xa and Xb should have the same number of rows.

Value

numerical value : the RV coefficient

Author(s)

Nicolas Robette

References

Escouffier, Y. (1973) Le traitement des variables vectorielles. Biometrics 29 751–760.

See Also

coiPCA, coiMCA, multiMCA

Examples

# 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)

Scaled deviations for a categorical supplementary variable

Description

From MCA results, computes scaled deviations between categories for a categorical supplementary variable.

Usage

scaled.dev(resmca, var)

Arguments

Value

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.

Author(s)

Nicolas Robette

References

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).

See Also

supvar, supvars, ggadd_supvar, ggadd_supvars, textvarsup, supind

Examples

# 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

Description

Performs a specific Multiple Correspondence Analysis, i.e. a variant of MCA that allows to treat undesirable categories as passive categories.

Usage

speMCA(data, excl = NULL, ncp = 5, row.w = NULL)

Arguments

Details

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.

Value

Returns an object of class speMCA, i.e. a list including:

Author(s)

Nicolas Robette

References

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).

See Also

getindexcat, ijunk, plot.speMCA, ggcloud_indiv, ggcloud_variables, csMCA

Examples

# 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))

Standardized MCA

Description

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.

Usage

stMCA(resmca, control)

Arguments

Details

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)

Value

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.

Author(s)

Nicolas Robette

References

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]

See Also

plot.stMCA

Examples

# 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))

Statistics for supplementary individuals

Description

From MCA results, computes statistics (coordinates, squared cosines) for supplementary individuals.

Usage

supind(resmca, supdata)

indsup(resmca, supdata)

Arguments

Value

Returns a list with the following items :

Note

indsup is softly deprecated. Please use supind instead.

Author(s)

Nicolas Robette

References

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).

See Also

ggadd_supind,textindsup, supvar, supvars

Examples

# 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])

Statistics for a categorical supplementary variable

Description

From MCA results, computes statistics (weights, coordinates, contributions, test-values, variances) for a categorical supplementary variable.

Usage

supvar(resmca, var)

varsup(resmca, var)

Arguments

Value

Returns a list:

Note

varsup is softly deprecated. Please use supvar instead.

Author(s)

Nicolas Robette

References

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).

See Also

supvars, ggadd_supvar, ggadd_supvars, textvarsup, supind

Examples

# 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)

Statistics for categorical supplementary variables

Description

From MCA results, computes statistics (weights, coordinates, squared cosines, contributions, test-values, variances) for categorical supplementary variables.

Usage

supvars(resmca, vars)

varsups(resmca, vars)

Arguments

Value

Returns a list with the following items :

Note

varsups is softly deprecated. Please use supvars instead.

Author(s)

Nicolas Robette

References

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).

See Also

supvar, ggadd_supvar, ggadd_supvars, textvarsup, supind

Examples

# 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")])

Table with the main contributions of categories to an axis

Description

Identifies the categories that contribute the most to a given dimension of a Multiple Correspondence Analysis and organizes these informations into a fancy table.

Usage

tabcontrib(resmca, dim = 1,
best = TRUE, limit = NULL,
dec = 2, shortlabs = FALSE)

Arguments

Value

A data frame with the following contributions.:

Author(s)

Nicolas Robette

References

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).

See Also

dimcontrib, dimdescr, dimeta2, dimtypicality

Examples

# 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)

Plot of supplementary individuals

Description

Adds supplementary individuals to a MCA cloud of the individuals.

Usage

textindsup(resmca, supdata, axes = c(1, 2), col = "darkred")

Arguments

Author(s)

Nicolas Robette

See Also

supind, plot.speMCA, plot.csMCA

Examples

# 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])

Plot of a categorical supplementary variable

Description

Adds a categorical supplementary variable to a MCA cloud of categories.

Usage

textvarsup(resmca, var, sel = 1:nlevels(var), axes = c(1, 2), 
           col = "black", app = 0, vname = NULL)

Arguments

Author(s)

Nicolas Robette

See Also

supvar, supvars, plot.speMCA, plot.csMCA

Examples

# 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)

Deprecated function

Description

This function has been moved to the translate.logit package.

Usage

translate.logit(...)

Arguments

Within-class MCA

Description

Within-class MCA, also called conditional MCA

Usage

wcMCA(data, class, excl = NULL, row.w = NULL, ncp = 5)

Arguments

Details

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.

Value

An object of class speMCA, with an additional item :

.

Note

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.

Author(s)

Nicolas Robette

References

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.)

See Also

MCAoiv, wcPCA, PCAoiv

Examples

# 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

Description

Within-class Principal Component Analysis

Usage

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))

Arguments

Details

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.

Value

An object of class PCA from FactoMineR package, with an additional item :

.

Note

The code is adapted from PCA function from FactoMineR package.

Author(s)

Nicolas Robette

References

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.)

See Also

PCAoiv, wcMCA, MCAoiv

Examples

# 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")

Deprecated functions

Description

These functions have been moved to the descriptio package. You may check its documentation here : https://nicolas-robette.github.io/descriptio/

Usage

wtable(...)

pem(...)

phi.table(...)

assoc.twocont(...)

assoc.twocat(...)

assoc.catcont(...)

assoc.yx(...)

darma(...)

catdesc(...)

condesc(...)

ggassoc_phiplot(...)

ggassoc_boxplot(...)

ggassoc_scatter(...)

ggassoc_crosstab(...)

Arguments