T. Meiser et al., ANALYZING HOMOGENEITY AND HETEROGENEITY OF CHANGE USING RASCH AND LATENT CLASS MODELS - A COMPARATIVE AND INTEGRATIVE APPROACH, Applied psychological measurement, 19(4), 1995, pp. 377-391
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.