Correspondence analysis used complementary to loglinear analysis

Loglinear analysis and correspondence analysis provide us with two different methods for the decomposition of contingency tables. In this paper we will show that there are cases in which these two techniques can be used complementary to each other. More specifically, we will show that often correspondence analysis can be viewed as providing a decomposition of the difference between two matrices, each following a specific loglinear model. Therefore, in these cases the correspondence analysis solution can be interpreted in terms of the difference between these loglinear models. A generalization of correspondence analysis, recently proposed by Escofier, will also be discussed. With this decomposition, which includes classical correspondence analysis as a special case, it is possible to use correspondence analysis complementary to loglinear analysis in more instances than those described for classical correspondence analysis. In this context correspondence analysis is used for the decomposition of the residuals of specific restricted loglinear models.