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.
Meiser, Thorsten; Hein-Eggers, Monika; Rompe, Pamela; Rudinger, Georg.
Analyzing homogeneity and heterogeneity of change using Rasch and latent class models: A comparative and integrative approach.
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