Joint correspondence analysis (JCA) by maximum likelihood

Parameter estimation in joint correspondence analysis (JCA) is typically performed by weighted least squares using the Burt matrix as the data matrix. In this paper, we show how to estimate the JCA model by means of maximum likelihood. For that purpose, JCA is defined as a model for the full K-way distribution by generalizing the correspondence analysis model for three-way tables proposed by Choulakian (1988a, 1988b). The advantage of placing JCA in a more formal statistical framework is that standard chi-squared tests can be applied to assess the goodness-of-fit of unrestricted and restricted models.