Standardized MCA

Performs a standardized Multiple Correspondence Analysis, i.e it takes MCA results and forces all the dimensions to be orthogonal to a supplementary "control" variable.

stMCA(resmca, control)

Arguments

resmca

an object of class MCA, speMCA, csMCA or multiMCA

control

a list of control variables

Details

Standardized MCA unfolds in several steps. 1. First, for each dimension of an input MCA, individual coordinates are used as dependent variable in a linear regression model and the 'control' variable is included as covariate in the same model. 2. The residuals from every models are retained and bound together. The resulting data frame is composed of continuous variables and its number of columns is equal to the number of dimensions in the input MCA. 3. Lastly, this data frame is used as input in a Principal Component Analysis.

It is exactly equivalent to MCA with one orthogonal instrumental variable (see MCAoiv)

Value

Returns an object of class stMCA. This object will be similar to resmca argument, still it does not comprehend modified rates, categories contributions and variables contributions.

References

Bry X., Robette N., Roueff O., 2016, « A dialogue of the deaf in the statistical theater? Adressing structural effects within a geometric data analysis framework », Quality & Quantity, 50(3), pp 1009–1020 [https://link.springer.com/article/10.1007/s11135-015-0187-z]

Author

Nicolas Robette

See also

plot.stMCA

Examples

# standardized MCA of Music example data set
# controlling for age
## and then draws the cloud of categories.
data(Music)
junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA")
mca <- speMCA(Music[,1:5], excl = junk)
stmca <- stMCA(mca, control = list(Music$Age))