Probit Latent Class Analysis with Dichotomous or Ordered Category Measures: Conditional Independence/Dependence Models

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Abstract
Flexible methods that relax restrictive conditional independence assumptions of latent classanalysis (LCA) are described. Dichotomous and ordered category manifest variables are viewed asdiscretized latent continuous variables. The latent continuous variables are assumed to have a mixtureofmultivariate-normals distribution. Within a latent class, conditional dependence is modeled as the mutual association of all or some latent continuous variables with a continuous latent trait (or in special cases, multiple latent traits). The relaxation of conditional independence assumptions allows LCA to better model natural taxa. Comparisons of specific restricted and unrestricted models permit statistical tests of specific aspects of latent taxonic structure. Latent class, latent trait, and latent distribution analysis can be viewed as special cases of the mixed latent trait model. The relationship between the multivariate probit mixture model proposed here and Rost’s mixed Rasch (1990, 1991) model is discussed. Two studies illustrate different uses of the proposed model.