GDAtools (version 2.1)

PCAiv: Principal Component Analysis with Instrumental Variables

Description

Principal Component Analysis with Instrumental Variables

Usage

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

Value

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

ratio

the share of inertia explained by the instrumental variables

.

Arguments

Y

data frame with only numeric variables

X

data frame of instrumental variables, which can be numeric or factors. It must have the same number of rows as Y.

row.w

Numeric vector of row weights. If NULL (default), a vector of 1 for uniform row weights is used.

ncp

number of dimensions kept in the results (by default 5)

Author

Nicolas Robette

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"

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")