What are discrete latent trait models?
Discrete latent trait models (Heinen, 1996) are a form of constrained LCA. Latent classes are assumed to have a unidimensional structure. For example, they may correspond to different levels of respondent ability, attitude, or disease severity, relative to an underlying continuum (latent trait). Two fairly similar approaches to discrete latent trait models exist, one based on logistic models (Lindsay, Clogg & Grego, 1991), and one based on probit models (Uebersax, 1993). Discrete latent trait models are often combined with unconstrained LCA to test whether the latent structure is unidimensional. Specifically, one compares model fit for an unconstrained LCA model with C latent classes to the fit of a unidimensional discrete latent trait model with C latent classes for the same data. If the difference G2 statistic for the comparison is nonsignificant, one concludes that the latent class structure is unidimensional Discrete latent trait models are also potentially helpful in problems of m
