This paper presents the generalized Hausman test to detect non-normality of the latent variable distribution in unidimensional Item Response Theory (IRT) models for binary data. The test is based on the estimators resulting from the two- parameter IRT model, that assumes normality of the latent variable, and the semi- nonparametric IRT model, that assumes a more flexible latent variable distribution. The performance of the test is evaluated through a simulation study, including the cases where the latent variable is generated from a skew-normal and mixture of nor- mals. The results highlight the good performance of the test when the latent variable is generated from a mixture of normals and from a skew-normal only with many items and large sample sizes.
A statistical test to assess the non - normality of the latent variable distribution / Lucia Guastadisegni; Irini Moustaki; Silvia Cagnone; Vassilis Vasdekis. - ELETTRONICO. - (2023), pp. 511-514. (Intervento presentato al convegno CLADAG 2023 tenutosi a Salerno nel September 11-13, 2023).
A statistical test to assess the non - normality of the latent variable distribution
Lucia Guastadisegni
;Silvia Cagnone;
2023
Abstract
This paper presents the generalized Hausman test to detect non-normality of the latent variable distribution in unidimensional Item Response Theory (IRT) models for binary data. The test is based on the estimators resulting from the two- parameter IRT model, that assumes normality of the latent variable, and the semi- nonparametric IRT model, that assumes a more flexible latent variable distribution. The performance of the test is evaluated through a simulation study, including the cases where the latent variable is generated from a skew-normal and mixture of nor- mals. The results highlight the good performance of the test when the latent variable is generated from a mixture of normals and from a skew-normal only with many items and large sample sizes.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.