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 as sumes homogeneity of change over persons. Using latent class models, s everal 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 appro ach by dividing the population of persons into classes that conform to Rasch models with class-specific parameters. Thus, qualitatively diff erent patterns of change can be modeled with the homogeneity assumptio n retained within each class, but not between classes. In contrast to the usual latent class approach, the mixed Rasch model includes a quan titative differentiation among persons in the same class. Thus, quanti tative differences in the level of the latent attribute are disentangl ed 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 develop ment in childhood and early adolescence, the existence of different de velopmental trajectories is demonstrated for two aspects of personalit y. Relations between the latent trajectories and discrete exogenous va riables are investigated.