A Hierarchy for Some Latent Structure Models

In this article we consider some latent variable models for dichotomous manifest variables that have recently appeared in sociology. The latent trait models considered are a logit/probit one-parameter, a logit/probit two-parameter, and a log-linear model. Some related latent class models for response consistency are also considered. We discuss both statistical and logical relations among these models and propose strategies for model selection, demonstrating those strategies in several examples. We also discuss the usefulness of the various models.