Description:
In this manuscript, the applicability of the Hausman test to the evaluation of itemresponse models is investigated. The Hausman test is a general test of model fit.The test assesses whether for a model in question the parameter estimates of twodifferent estimators coincide. The test can be implemented for item response modelsby comparing the parameter estimates of the marginal maximum likelihood estimatorwith the corresponding parameter estimates of a limited information estimator. For acorrectly specified item response model, the difference of the two estimates is normallydistributed around zero. The Hausman test can be used for the evaluation of item fitand global model fit. The performance of the test is evaluated in a simulation study.The simulation study suggests that the implemented versions of the test adhere to thenominal Type-I error rate well in samples of 1000 test takers and more. The test is alsocapable to detect misspecified item characteristic functions, but lacks power to detectviolations of the conditional independence assumption.