Pearson and Log-likelihood Chi-square Test of Fit for Latent Class Analysis Estimated with Complex Samples

In this note we discuss model fit evaluation for the Latent Class Analysis (LCA) model under complex sampling. Suppose that for the i− individual in the sample we observe r categorical/discrete variables Ui1, ..., Uir. Suppose that for individual i there exist one unobserved categorical variable Ci, called the latent class variable. The LCA model is described by the following equations P (Uij = l|Ci = k) = plk