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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
Effective date (Start): September 19, 2017
Effective date (End): 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
Research place: 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)

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