Performance of the bootstrap Rasch model test under violations of non-intersecting item response functions

The Rasch model is known in particular for its properties of parameter separability and specific objectivity. The extent to which this property is attained depends on the magnitude of the discrepancy between the data and the model. The use of reliable model fit tests which can detect model violations is therefore essential before a psychological test is used and inferences based on the requirements of the Rasch model are drawn. This paper provides a critical analysis of the performance of the parametric bootstrap model test (von Davier, 1997) in the presence of non-parallel item response functions as violations of a basic requirement of the dichotomous Rasch model. Based on results from simulated data it is shown that in general the bootstrap test leads too often to failures to reject non-fitting data.