On the Applicability of some IRT Models for Repeated Measurement Designs: Conditions, Consequences, and Goodness-of-Fit Tests

Two structural Rasch models for repeated measurement designs, LLTM and LLRA, are analyzed with respect to the underlying model assumptions. It will be shown in which ways both models involve non-trivial properties like local stochastic independence, generalizability over items and persons, and generalizability of item discrimination coefficients over items. Especially matters of independence were hardly discussed yet. For all types of model deviations, goodness-of-fit tests are given. That these tests may be useful for practical applications is demonstrated by means of two empirical data sets.