Bootstrap confidence regions for correspondence analysis

Abstract

A bootstrap-based method for constructing confidence regions (CRs) around row or column points projected onto a pair of axes from the correspondence analysis (CA) of a two-way contingency table is presented. These regions deal with the specific question of the sampling variation of sample row and column profile points around population row and column profile points when both are projected onto the observed axes, rather than the decomposition of the χ2-test of independence or the general question of the stability of the observed CA display which has been considered in previous work. The method therefore constructs the regions in a different way to what has been proposed before. A simulation experiment shows that the method performs well in most of the situations in which it might be used, with a few exceptions being noted. An example illustrates that the method produces conclusions which are consistent with those from detailed parametric modelling.