Modelos alternativos da TRI para dados politômicos

Abstract

The item response theory (IRT) models for polytomous data are frequently used in the analysis of data coming from the behavioral and social sciences. From a practical point of view, polytomous data are more informative than dichotomous data, since it considers more than two response categories in each test item, making the models assigned to this type of data attractive. The purpose of this research is to explore alternative polytomous IRT models and their multidimensional extensions, filling some gaps in the literature. Specifically, the chapters of this work follow a construction sequence of IRT modeling. Firstly, we conducted a study to assist readers in choosing between two of the major polytomous IRT models in the one-dimensional context: the graded response (GR) model and the generalized partial credit (GPC) model. We conducted a sensitivity analysis of priors to choose a suitable priors scenario for each model and we verified the performance of some model comparison criteria against these models through a simulation study. Then, we extend the one-dimensional GPC model to the bifactor context, proposing the GPC-bifactor model, in which a global latent trait and specific latent traits are considered through an additive structure in its formulation. In addition, we flexibilize the structure of the GPC-bifactor model, making possible its use with other link functions beyond the usual logit, such as probit and clog-log. Then, we incorporate the relation between the items and the latent trait dimensions of the individuals in the formulation of the multidimensional item response theory (MIRT) models through the Q-matrix, a component present in the vast majority of cognitive diagnostic models (CDM), making it easy for users to express the item-trait relationship in MIRT models. Finally, we propose a validation method using the Q-matrix in MIRT models. In particular, we used in the study the multidimensional GPC model with Q-matrix embedded in its formulation. The different simulation studies and the applications performed in this research showed that these models are alternative models for the analysis of polytomous data and that can be used by the users in practice.