Some useful extensions of the usual correspondence analysis approach and the usual log-linear models approach to the analysis of contingency tables (with discussion and reply).

This paper is an expanded version of an invited paper presented by the author at the 45th Session of the International Statistical Institute in Amsterdam, Netherlands. It describes how correspondence analysis models can serve as an extension of the usual log-linear models approach, and how log-bilinear models can serve as an extension of the usual log-linear models approach, in the analysis of contingency tables. Relationships between the correspondence analysis models and the log-bilinear models are also noted. The correspondence analysis models can be used to simplify and supplement results obtained with the usual correspondence analysis approach, and the log-bilinear models can be used to simplify and supplement results obtained with the usual log-linear approach. Modifications of the usual approaches are recommended here with respect to both descriptive and inferential aspects of these approaches.