Abstract: This paper will illustrate how a number of educational testing models may be formalized as constrained (using inequality and equality constraints) latent class models. The parameters of these models will be estimated using an application of the Gibbs sampler. The goodness of fit of these models will be determined using (pseudo) likelihood ratio tests evaluated via posterior predictive P-values. The feasibility of both the estimation and testing procedures will be illustrated via the analysis of a number of simulated data sets.
Key words and phrases: Discrepancy measure, Gibbs sampler, inequality constraints, latent class analysis, latent class models, posterior predictive P-values, pseudo likelihood ratio, robust goodness-of-fit test.