Analyzing homogeneity and heterogeneity of change using Rasch and latent class models: A comparative and integrative approach

Abstract

The application of unidimensional Rasch models to longitudinal data assumes homogeneity of change over persons. Using latent class models, several classes with qualitatively distinct patterns of development can be taken into account; thus, heterogeneity of change is assumed. The mixed Rasch model integrates both the Rasch and the latent class approach by dividing the population of persons into classes that conform to Rasch models with class-specific parameters. Thus, qualitatively different patterns of change can be modeled with the homogeneity assumption retained within each class, but not between classes. In contrast to the usual latent class approach, the mixed Rasch model includes a quantitative differentiation among persons in the same class. Thus, quantitative differences in the level of the latent attribute are disentangled from the qualitative shape of development. A theoretical comparison of the formal approaches is presented here, as well as an application to empirical longitudinal data. In the context of personality development in childhood and early adolescence, the existence of different developmental trajectories is demonstrated for two aspects of personality. Relations between the latent trajectories and discrete exogenous variables are investigated. Index terms: latent class analysis, latent structure analysis, measurement of change, mixture distribution models, Rasch model, rating scale model.