B0359
Title: A novel test for detecting non-normality of the latent variable distribution with binary outcomes
Authors: Lucia Guastadisegni - University of Bologna (Italy) [presenting]
Silvia Cagnone - University of Bologna (Italy)
Irini Moustaki - London School of Economics (United Kingdom)
Vassilis Vasdekis - Athens University of Economics and Business/Research Center (Greece)
Abstract: In the context of unidimensional item response theory (IRT) models, the assumption of a standard normal distribution for the latent variable can lead to biased parameter estimates when the true distribution of the latent variable deviates from the normal shape, especially with binary outcomes. The generalized Hausman test is extended for detecting non-normality in the distribution of the latent variable in unidimensional IRT models for binary data. The test builds upon two estimation approaches: the pairwise maximum likelihood estimator of the classical unidimensional IRT model, which assumes normality of the latent variable, and the quasi-maximum likelihood estimator of the unidimensional semi-nonparametric IRT model, which allows for a more flexible latent variable distribution. The performance of the proposed test is evaluated through a simulation study, comparing it with the likelihood-ratio test and the $M_2$ test. Additionally, some information criteria are computed. The simulation results show that the generalized Hausman test outperforms the other tests under most conditions, indicating its effectiveness in detecting the non-normality of the latent variable distribution. Information criteria present contradictory results under certain conditions.
