Between-class MCA

Between-class MCA, also called Barycentric Discriminant Analysis

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

Arguments

data: data frame with only categorical variables, i.e. factors
class: factor specifying the class
excl: 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").
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

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 :

ratio: the between-class inertia percentage

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.)

Author

Nicolas Robette

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"))
#> Warning: ggrepel: 26 unlabeled data points (too many overlaps). Consider increasing max.overlaps

# between-class inertia percentage
res$ratio
#> [1] 0.03346136