PCA with categorical variables: Multiple correspondence analysis

5 functions to do Multiple Correspondence Analysis in R

This mentions the ade4 package, and factominer


The factorminer package also does mca

FactoMineR: Multiple Correspondence Analysis



Multiple Correspondence Analysis Essentials: Interpretation and application to investigate the associations between categories of multiple qualitative variables – R software and data mining



I think this is the reference that might be the origin of PCA w/ categorical variables in ecology related fields


Hill & Smith 1976 Principal component analysis of taxonomic data with multistate discrete characters


The package ade4 has a function dudi.mca() for multiple correspondence analysis (PCA w/categorical variables) and dudi.hillsmith() which allows you to do a mix; its probably similar to that PCAmix package I sent.  ade4 is part of a suite of packages by crazy French ecologists that are REALLY into multivariate stuff- I find most of the documentation really hard to understand (lots of math, not much ecology, not perfect English).  They have a paper “The ade4 package: implementing the duality diagram for ecologists” In the Journal for Statistical Software which has a section “4. An example: dudi.hillsmith” where they analyze the “dune meadow” dataset that shows up often in vegan I think.  This example, whether analyzed with dudi.hillmsith or the functions in the PCAmix package (or whatever its name is) might be a good place to start.

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