An extended study into the relationship between correspondence analysis and latent class analysis

Researchers dealing with frequency data today can choose from a vast range of methods, descriptive and inferential. Two such well-known and useful methods are correspondence analysis and latent class analysis. Although these two methods were initially used for different research objectives, they are mathematically related to each other. Relations between these methods, however, have only been reported in the literature regarding the bivariate case. In this paper, we extend the study of such relations to the multivariate case. In particular the multivariate X latent class model is shown to imply the (relatively new) joint multivariate correspondence model with X - 1 positive eigenvalues. Such relations allow the underlying methods to be treated as variants of the same conceptual idea, providing some new meaningful aspects, which may help researchers better interpret the findings of their investigation.