This paper introduces the generalized Hausman test as a novel method for detecting non-normality of the latent variable distribution of unidimensional Item Response Theory (IRT) models for binary data. The test utilizes the pairwise maximum likelihood estimator obtained for the parameters of the classical two-parameter IRT model, which assumes normality of the latent variable, and the quasi-maximum likelihood estimator obtained under a semi-nonparametric framework, allowing for a more flexible distribution of the latent variable. The performance of the generalized Hausman test is evaluated through a simulation study and it is compared with the likelihood-ratio and the M2 test statistics. Additionally, various information criteria are computed. The simulation results show that the generalized Hausman test outperforms the other tests under most conditions. However, the results obtained from the information criteria are somewhat contradictory under certain conditions, suggesting a need for further investigation and interpretation.

翻译：本文提出将广义Hausman检验作为一种新方法，用于检测二元数据单维项目反应理论（IRT）模型中潜在变量分布的非正态性。该检验利用经典双参数IRT模型（假设潜在变量服从正态分布）的参数所对应的成对极大似然估计量，以及在半非参数框架下得到的拟极大似然估计量，后者允许潜在变量具有更灵活的分布形式。通过模拟研究评估广义Hausman检验的表现，并将其与似然比检验和M2检验统计量进行比较。此外，还计算了多种信息准则。模拟结果表明，广义Hausman检验在大多数条件下优于其他检验方法。然而，在某些条件下信息准则的结果略显矛盾，表明需要进一步的研究与解读。