An Evaluation of Overall Goodness-of-Fit Tests for the Rasch Model

For assessing the fit of item response theory models, it has been suggested to apply overall goodness-of-fit tests as well as tests for individual items and item pairs. Although numerous goodness-of-fit tests have been proposed in the literature for the Rasch model, their relative power against several model violations has not been investigated so far. This study compares four of these tests, which are all available in R software: T ₁₀, T ₁₁, M ₂, and the LR test. Results on the Type I error rate and the sensitivity to violations of different assumptions of the Rasch model (unidimensionality, local independence on the level of item pairs, equal item discrimination, zero as a lower asymptote for the item characteristic curves, invariance of the item parameters) are reported. The results indicate that the T ₁₁ test is comparatively most powerful against violations of the assumption of parallel item characteristic curves, which includes the presence of unequal item discriminations and a non-zero lower asymptote. Against the remaining model violations, which can be summarized as local dependence, M ₂ is found to be most powerful. T ₁₀ and LR are found to be sensitive against violations of the assumption of parallel item characteristic curves, but are insensitive against local dependence.