Multiple Correspondence Analysis with Instrumental Variables
MCAiv(Y, X, excl = NULL, row.w = NULL, ncp = 5)
data frame with only factors
data frame of instrumental variables, which can be numeric or factors. It must have the same number of rows as
numeric vector indicating the indexes of the "junk" categories (default is NULL). See
getindexcat or use
ijunk interactive function to identify these indexes. It may also be a character vector of junk categories, specified in the form "namevariable.namecategory" (for instance "gender.male").
Numeric vector of row weights. If NULL (default), a vector of 1 for uniform row weights is used.
number of dimensions kept in the results (by default 5)
Multiple Correspondence Analysis with Instrumental Variables consists in three steps :
1. Specific MCA of
Y, keeping all the dimensions of the space
2. Computation of one linear regression for each dimension in the specific MCA, with individual coordinates as response and all variables in
X as explanatory variables.
3. Principal Component Analysis of the set of predicted values from the regressions in 2.
Multiple Correspondence Analysis with Instrumental Variables is also known as "Canonical Correspondence Analysis" or "Constrained Correspondence Analysis".
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.
An object of class
FactoMineR package, with
X as supplementary variables, and an additional item :
the share of inertia explained by the instrumental variables
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.)