Bayesian dimensionality assessment for the multidimensional nominal response model
EntityUAM. Departamento de Psicología Social y Metodología
10.3389/fpsyg.2017.00961Frontiers in Psychology 8 (2017): 961
Funded byThis research was partially supported by grants PSI2012-31958 and PSI2015-66366-P from the Ministerio de Economía y Competitividad (Spain)
ProjectGobierno de España. PSI2015-66366-P; Gobierno de España. PSI2012-31958
SubjectsMultidimensional nominal response model; Multidimensional item response theory; Standardized generalized discrepancy measure; WAICC; LOO; Bayesian inference; Psicología
Esta obra está bajo una Licencia Creative Commons Atribución 4.0 Internacional.
This article introduces Bayesian estimation and evaluation procedures for the multidimensional nominal response model. The utility of this model is to perform a nominal factor analysis of items that consist of a ﬁnite number of unordered response categories. The key aspect of the model, in comparison with traditional factorial model, is that there is a slope for each response category on the latent dimensions, instead of having slopes associated to the items. The extended parameterization of the multidimensional nominal response model requires large samples for estimation. When sample size is of a moderate or small size, some of these parameters may be weakly empirically identiﬁable and the estimation algorithm may run into difﬁculties. We propose a Bayesian MCMC inferential algorithm to estimate the parameters and the number of dimensions underlying the multidimensional nominal response model. Two Bayesian approaches to model evaluation were compared: discrepancy statistics (DIC, WAICC, and LOO) that provide an indication of the relative merit of different models, and the standardized generalized discrepancy measure that requires resampling data and is computationally more involved. A simulation study was conducted to compare these two approaches, and the results show that the standardized generalized discrepancy measure can be used to reliably estimate the dimensionality of the model whereas the discrepancy statistics are questionable. The paper also includes an example with real data in the context of learning styles, in which the model is used to conduct an exploratory factor analysis of nominal data
Google Scholar:Revuelta Menéndez, Javier - Ximénez, Carmen
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