PCAiv {GDAtools} | R Documentation |
Principal Component Analysis with Instrumental Variables
Description
Principal Component Analysis with Instrumental Variables
Usage
PCAiv(Y, X, row.w = NULL, ncp = 5)
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 |
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) |
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 :
ratio |
the share of inertia explained by the instrumental variables |
.
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
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")