Full text
| |
| Author(s): |
Juan Leonardo Padilla Gómez
Total Authors: 1
|
| Document type: | Doctoral Thesis |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2018-03-20 |
| Examining board members: |
Caio Lucidius Naberezny Azevedo;
Filidor Edilfonso Vilca Labra;
Dalton Francisco de Andrade;
Heliton Ribeiro Tavares;
Mariana Curi
|
| Advisor: | Caio Lucidius Naberezny Azevedo |
| Abstract | |
This work consists of four major parts, which correspond to contributions related to Item Response Theory (IRT), regarding item response function modeling, latent traits distribution modeling, model fit assessment and model selection. In the first part, we propose new versions of the univariate and multivariate centered skew-t distributions, which are named Centered Skew-t (CSt) distributions. They extend the works of Azzalini (1985) and Padilla (2014) and represent interesting alternatives to the work of Arellano-Valle and Azzalini (2013). Based on the univariate version of the Cst distribution, a linear regression model with errors following such distribution was proposed. Also, we define a new link function for binary data analysis based on the proposed distribution. We develop estimation methods under a fully Bayesian perspective and present simulation studies in order to verify the performance of the proposed approaches, as well as real data analyses. The results indicate that the developed methodologies perform quite well. In the second part we extend the model classes proposed in Padilla (2014), Santos et al. (2013) and Bazán et al. (2006), considering situations in which the subjects belong to different groups and they are submitted to different unidimensional or multidimensional (that measures more than one latent trait) tests with dichotomous (or dichotomized) items. The approach consists of using the CSt distribution to define the Item Response Function (IRF) and to model the distribution of the latent traits. We develop estimation methods, model fit assessment and model comparison tools, based on a fully Bayesian approach, through Markov Chain Monte Carlo (MCMC) algorithms using augmented likelihoods (augmented data). We carry out simulation studies to assess the performance of the proposed models/algorithms under different scenarios of practical interest. The results indicate that the proposed methodologies provide satisfactory results. Applications on real data sets are also presented. In the third part, we extend the IRT models previously developed, to allow them to use available collateral information (Associated Factors), as gender or desired course, as it happens on the admissions exams of some universities. Simulation studies and applications on real data sets are presented, where we verified the satisfactory behavior of the proposed methodologies. Finally, we present some contributions related to mechanisms of model fit assessment and comparison, through techniques based on residual analysis, posterior predictive model checking and RJMCMC (Reversible Jump MCMC) algorithms. These tools were also evaluated through appropriate simulation studies (AU) | |
| FAPESP's process: | 13/26336-5 - Bayesian inference for multidimensional item response models under heavy tail skewed latent trait distributions and link functions |
| Grantee: | Juan Leonardo Padilla Gomez |
| Support Opportunities: | Scholarships in Brazil - Doctorate |