Analyzing the Fit of IRT Models With the Hausman Test

In this manuscript, the applicability of the Hausman test to the evaluation of item response 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 two different estimators coincide. The test can be implemented for item response models by comparing the parameter estimates of the marginal maximum likelihood estimator with the corresponding parameter estimates of a limited information estimator. For a correctly specified item response model, the difference of the two estimates is normally distributed around zero. The Hausman test can be used for the evaluation of item fit and 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 the nominal Type-I error rate well in samples of 1000 test takers and more. The test is also capable to detect misspecified item characteristic functions, but lacks power to detect violations of the conditional independence assumption.