Considering variable selection criteria in correspondence analysis

Ordinary goodness of fit criteria in correspondence analysis are considered as variable selection criteria in case correspondence analysis which is one of multivariate methods without external variables can be applied. The goodness of fit criteria focused here are proportion of cumulative eigenvalues, proportion of cumulative squared-eigenvalues and proportion of cumulative off-diagonal fitness. Each criterion is applied to a couple of real data sets and evaluated with interpretation of the selection process and result (selected subset of variables). Four selection procedures such as backward elimination and forward-backward selection are also performed to compare with each other as well as with all possible selection procedure. These results illustrate that the criteria can be used as selection criteria to select a subset of variables in correspondence analysis and to assess categorical items (questions) in a survey (questionnaire).