Correspondence analysis of contingency tables with subpartitions on rows and columns

Abstract

We present Intra-Table Correspondence Analysis using two approaches:Correspondence Analysis with respect to a model and Weighted PrincipalComponent Analysis. In addition, we use the relationship between CorrespondenceAnalysis and the Log-Linear Models to provide a deeper insightinto the interactions that each Correspondence Analysis describes. Wedevelop in detail the Internal Correspondence Analysis as an Intra-TableCorrespondence Analysis in two dimensions and introduce the Intra-blocksCorrespondence Analysis. Moreover, we summarize the superimposed representationsand give some aids to interpret the graphics associated to thesubpartition structures of the table. Finally, the methods presented in thiswork are illustrated by their application to the standardized public test datacollected from Colombian secondary education students in 2008.