Asymmetric multidimensional Item response theory models: estimation and diagnostic methods under a Bayesian perspective

Abstract

This project aims to develop and implement diagnostic techniques for the studied models in the related doctoral FAPESP project (process No. 2013/26336-5). We will consider residual analysis, adapting some useful residuals considered in the literature, see (FARIAS; BRANCO et al., 2012) and (SANTOS, 2015), which were used for other regression models. In particular we focus on the quantile residuals, see (SMITH, 1985) and (DUNN; SMYTH, 1996), and different alternatives of the latent residuals. The techniques of posterior predictive model checking through some appropriated discrepancy measures, as in (AZEVEDO; ANDRADE; FOX, 2012), (LEVY; MISLEVY; SINHARAY, 2009), (SANTOS; AZEVEDO; BOLFARINE, 2013) and (AZEVEDO; FOX; ANDRADE, 2013), will be used too. We will explore techniques for the determination of the dimensionality based on the tetrachoric correlation matrices as well as the proposal of (NOJOSA, 2010), based on algorithms RJMCMC, for dimensionality assessment. Simulation studies and real data analyses will be performed. (AU)