Modeling Qualitative Variation Within Latent Trait Dimensions: Application of Mixed-Measurement to Personality...

The mixed-measurement IRT model and the traditional factor analytic model are two fundamentally different ways of representing the structure underlying an item response matrix. To contrast these approaches, the parameters of full-information item factor models of varying dimensionality and mixed-measurement models of varying numbers of latent classes were estimated in a sample of 1,000 responses to a 14-item measure of Positive Interpersonal Engagement. Findings indicated that either a two latent factor or a two latent class mixed-model provided the most appropriate representation of the data. We also found that the factor models were, in general, more parsimonious than the mixed-measurement models. Nevertheless, we argue that deciding between a dimensional and a mixed- measurement representation of item response heterogeneity should not rest solely on statistical criteria. In the discussion, we suggest some research contexts in which the mixed- measurement model may be conceptually more appropriate than the traditional factor model.