A comparison between different methods of analysis for the residuals in a contingency table, and a new index measure

In 1994, Rudas, Clogg and Lindsay proposed a new index of lack of fit for a certain model H in contingency table analysis. The framework of the index is a two latent class model where the model H applies to the first latent class and the second latent class is unrestricted. The index of lack of fit is the proportion of individuals of the population intrinsically outside the model. In this work we propose the analysis of the second latent class to study the causes of lack of fit of a model and to detect outlying cells. By means of three classical examples from the literature Rudas' second latent class analysis is compared to standardized residual analysis, the deleted residual analysis, and the variations of likelihood ratio statistics. The second latent class was not worse than any other criterion in the three examples.