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

• Grant number: 17/05326-2
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: September 19, 2017
• End date: January 25, 2018
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Caio Lucidius Naberezny Azevedo
• Grantee: Juan Leonardo Padilla Gomez
• Supervisor: Anne Corinne Manley
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: University of Florida, Gainesville (UF), United States
• Associated to the scholarship: 13/26336-5 - Bayesian inference for multidimensional item response models under heavy tail skewed latent trait distributions and link functions, BP.DR

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)