Discovering Heterogeneity: Continuous Versus Discrete Latent Variables

In the case of the 2 x 2 x2 table resulting form a three-wave panel study, Converse's "black-and-white" model, with discrete latent classes, and the Rasch continous latent-trait model cannont be distinguished. When the reponse is trichotomous, the resulting 3 x 3 x 3 table provides information on heterogeneity of respondents that is detected in different ways by these two kinds of models. Different kinds of heterogeneity, leading to models with different numbers of latent classes or different numbers of latent traits, can be distinguished within both approaches. The two approaches also yield distinctive accounts of change in response probabilities. Data from the American Panel Study illustrate how comparisons between the two kinds of models can be effected.