Contribuições para modelos de diagnóstico cognitivo

Abstract

Cognitive Diagnostic Models (CDMs) are latent variable models which are useful for identifying the profile of respondents through tests or assessments. They are mainly used in educational assessments, but can also be considered to analyze other types of latent variables, including personality traits and other areas in psychometrics, as well as any type of data that fits in item analysis. Unlike the Item Response Theory (IRT) models, in which the latent variable is continuous, in an CDM the latent variable is discrete, however, the responses can have multiple formats. The purpose of this research is to contribute to the CDMs state of the art, filling gaps that still exist, with special emphasis on the CDMs under a Bayesian approach. The chapters of this thesis follow a sequence of construction of CDMs for different types of response variables. First, a collaborative study with the dichotomous DINA model, already present in the literature, is shown, aiming at a better understanding of the CDMs and showing a comparison of estimation methods already explored with a new MCMC method, through the No-U-Turn Sampler algorithm (NUTS). Simulation studies are shown and the methodology is used for an application in the mental health area. Next, considering continuous responses, we develop the extension of the DINA model for this type of response (C-DINA), under a Bayesian approach, carrying out a priors sensitivity study and evaluating the performance of the methodology through simulation studies, as well as providing a more detailed explanation of the construction logic behind models of this class and showing an application related to risk perception. Then, we propose a CDM for limited responses in the unit interval (B-DINA), which is unprecedented in the literature, explaining the details of its formulation and estimation, under a Bayesian approach, evaluating the recovery of parameters of the proposed estimation methodology through a simulation study and also showing the potential of its use in an application for social-demographic data. Finally, we propose new probability distributions for random variables limited to the unit interval, with the development of quantile regression for mixed-effects models, carrying out simulation studies and an application for extreme poverty data. The different simulation and application studies throughout the text show that the proposals bring good results and have the potential to be used by researchers from different areas, with the codes used to estimate the parameters also made available.