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Bayesian inference for multidimensional item response models under heavy tail skewed latent trait distributions and link functions

Grant number: 13/26336-5
Support type:Scholarships in Brazil - Doctorate
Effective date (Start): April 01, 2014
Effective date (End): March 31, 2018
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics
Principal Investigator:Caio Lucidius Naberezny Azevedo
Grantee:Juan Leonardo Padilla Gomez
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:12/21788-2 - Regression models and applications, AP.TEM
Associated scholarship(s):17/05326-2 - Asymmetric multidimensional Item Response Theory models: estimation and diagnostic methods under a Bayesian perspective, BE.EP.DR


This project aims to extend the classes of multidimensional Item Response Theory models already considered in the literature. We will consider the scenario where subjects, belonging to different groups, answer multidimensional tests (in a broad sense of the word) with dichotomous items (or dichotomized). Such tests can be different from each other but they must present some structure of common items. Additionally, it will be considered available collateral information (associated factors), in the modeling of the latent traits, such as gender or intended course, as occurs at admissional tests, for example. The modeling will correspond to: the using of a version the multivariate centered skew Student t distribution (to be developed and studied) to model the latent traits, a link function based on the univariate centered skew normal distribution, adding a level in the whole modeling by using a regression structure in order to relate the latent traits and their associated factors. It will be developed bayesian mechanisms for both estimation and model validation. Also, it will be considered simulation studies and real data analysis.