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.
Lucia Guastadisegni, Irini Moustaki, Vassilis Vasdekis, Silvia Cagnone (2023). Detecting Latent Variable Non-normality Through the Generalized Hausman Test. XXX : Springer Proceedings in Mathematics & Statistics [10.1007/978-3-031-27781-8_10].
Detecting Latent Variable Non-normality Through the Generalized Hausman Test
Lucia Guastadisegni
;Silvia Cagnone
2023
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.