PCA: Principal Component Analysis (PCA)

Description

Performs Principal Component Analysis (PCA) with supplementary individuals, supplementary quantitative variables and supplementary categorical variables.
Missing values are replaced by the column mean.

Usage

PCA(X, scale.unit = TRUE, ncp = 5, ind.sup = NULL, 
    quanti.sup = NULL, quali.sup = NULL, row.w = NULL, 
    col.w = NULL, graph = TRUE, axes = c(1,2))

Value

Returns a list including:

eig: a matrix containing all the eigenvalues, the percentage of variance and the cumulative percentage of variance
var: a list of matrices containing all the results for the active variables (coordinates, correlation between variables and axes, square cosine, contributions)
ind: a list of matrices containing all the results for the active individuals (coordinates, square cosine, contributions)
ind.sup: a list of matrices containing all the results for the supplementary individuals (coordinates, square cosine)
quanti.sup: a list of matrices containing all the results for the supplementary quantitative variables (coordinates, correlation between variables and axes)
quali.sup: a list of matrices containing all the results for the supplementary categorical variables (coordinates of each categories of each variables, v.test which is a criterion with a Normal distribution, and eta2 which is the square correlation corefficient between a qualitative variable and a dimension)

Returns the individuals factor map and the variables factor map.

The plots may be improved using the argument autolab, modifying the size of the labels or selecting some elements thanks to the plot.PCA function.

Arguments

X: a data frame with n rows (individuals) and p columns (numeric variables)
ncp: number of dimensions kept in the results (by default 5)
scale.unit: a boolean, if TRUE (value set by default) then data are scaled to unit variance
ind.sup: a vector indicating the indexes of the supplementary individuals
quanti.sup: a vector indicating the indexes of the quantitative supplementary variables
quali.sup: a vector indicating the indexes of the categorical supplementary variables
row.w: an optional row weights (by default, a vector of 1 for uniform row weights); the weights are given only for the active individuals
col.w: an optional column weights (by default, uniform column weights); the weights are given only for the active variables
graph: boolean, if TRUE a graph is displayed
axes: a length 2 vector specifying the components to plot

Author

Francois Husson Francois.Husson@agrocampus-ouest.fr, Jeremy Mazet

References

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

Examples

Run this code

data(decathlon)
res.pca <- PCA(decathlon, quanti.sup = 11:12, quali.sup=13)
## plot of the eigenvalues
## barplot(res.pca$eig[,1],main="Eigenvalues",names.arg=1:nrow(res.pca$eig))
summary(res.pca)
plot(res.pca,choix="ind",habillage=13)
if (FALSE) {
## To describe the dimensions
dimdesc(res.pca, axes = 1:2)

## To draw ellipses around the categories of the 13th variable (which is categorical)
plotellipses(res.pca,13)

## Graphical interface
require(Factoshiny)
res <- Factoshiny(decathlon)

## Example with missing data
## use package missMDA
require(missMDA)
data(orange)
nb <- estim_ncpPCA(orange,ncp.min=0,ncp.max=5,method.cv="Kfold",nbsim=50)
imputed <- imputePCA(orange,ncp=nb$ncp)
res.pca <- PCA(imputed$completeObs)
}

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