Analyzing Homogeneity and Heterogeneity of Change Using Rasch and Latent Class Models: A Comparative and Integrative Approach

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 develop ment can be taken into account; thus, heterogeneity of change is assumed. The mixed Rasch model inte grates both the Rasch and the latent class approach by dividing the population of persons into classes that conform to Rasch models with class-specific param eters. Thus, qualitatively different patterns of change can be modeled with the homogeneity assumption re tained 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 dis entangled 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 de velopment in childhood and early adolescence, the existence of different developmental trajectories is demonstrated for two aspects of personality. Rela tions between the latent trajectories and discrete exogenous variables are investigated.