Contribuições para modelos gerais de diagnóstico cognitivo

Abstract

Cognitive Diagnosis Models (CDMs) are discrete latent variable models that aim to determine an individual's pattern of possession of skills or attributes based on their test responses. This class includes the general diagnosis models, whose formulation allows various other CDMs to be obtained as a special case of the former. This work presents contributions to these general models under a Bayesian approach.

First, we present Bayesian formulations for two general diagnosis models, the Generalized DINA (G-DINA) model, designed for dichotomous responses; and the General Polytomous Diagnosis Model (GPDM), designed for polytomous responses. These formulations include new sets of constraints on the item parameters to improve the estimation and interpretability of the model parameters. For both models, an estimation method was implemented using the JAGS software, which is available in this thesis. Moreover, for both models, a simulation study was designed to evaluate the parameters recovery accuracy of this Bayesian estimation method and the results were compared with those obtained with the standard classical estimation method. In both studies, the results indicate that the proposed Bayesian estimation method recovers all parameters with accuracy equal to or better than the classical estimation method under the evaluated scenarios.

In an example of application, we use the proposed models to examine the responses of 1111 college students to the Beck Depression Inventory (BDI) using a CDM in the modeling process. In the first instance, we compare the results obtained with the DINA model (adopted in the original formulation of this methodology) and the G-DINA model, both applied to the dichotomized data. In the second instance, we compare the results obtained with the G-DINA model, applied to dichotomized data, and the GPDM, applied to original polytomous data.

At last, in another example of application, we present a new recommendation system for movies that incorporates a CDM in its formulation. The CDM is used to predict the ratings that a user would give to each item and make recommendations based on these predictions. The proposed method was applied to two movie datasets and its performance compared to other recommendation systems found in the literature, presenting results superior to the competing methods.