Nonnormality in Latent Trait Modeling

This chapter presents tools to facilitate specific tests on three sources of nonnormality in subtest scores or latent response variates: nonnormality of the latent trait, heteroscedasticity of the manifest variable residuals, and level dependency of the factor loadings. It outlines factor model and discusses existing approaches to test for each of the three sources of nonnormality. The chapter also outlines a unified approach in which the different sources of nonnormality are tested simultaneously. It also discusses examples in which the models are applied to intelligence subtest scores, and to affective analyzing item scores. It analyzes ordinal item level data from a personality questionnaire. The chapter utilizes specific functional forms for the relation between the latent trait on the one side and the residuals variances and the factor loadings on the other side. The develpoment of nonparametric approaches could ideally be combined into a single model with existing nonparametric approaches to modeling the latent trait distribution.