Detecting latent variable non-normality through the generalized Hausman test

This paper extends the generalized Hausman test to detect non-normality of the latent variable distribution in unidimensional IRT models for binary data. To build the test, we consider the estimator obtained from the two-parameter IRT model, that assumes normality of the latent variable, and the estimator obtained under a semi-nonparametric framework, that allows for a more flexible latent variable distribution. The behaviour of the test is evaluated through a simulation study. The results highlight the good performance of the test in terms of both Type I error rates and power with many items and large sample sizes.