A Two-Stage Conditional Estimation Procedure for Unrestricted Latent Class Models

A variety of latent class models has been presented during the last 10 years which are restricted forms of a more general class of probability models. Each of these models involves an a priori dependency structure among a set of dichotomously scored tasks that define latent class response patterns across the tasks. In turn, the probabilities related to these latent class patterns along with a set of “Omission” and “intrusion” error rates for each task are the parameters used in defining models within this general class.

One problem in using these models is that the defining parameters for a specific model may not be “identifiable.” To deal with this problem, researchers have considered curtailing the form of the model of interest by placing restrictions on the defining parameters.

The purpose of this paper is to describe a two-stage conditional estimation procedure which results in reasonable estimates of specific models even though they may be nonidentifiable. This procedure involves the following stages: (a) establishment of initial parameter estimates and (b) step-wise maximum likelihood solutions for latent class probabilities and classification errors with iteration of this process until stable parameter estimates across successive iterations are obtained.