Modelos da teoria da resposta ao item hierárquicos sob amostragem informativa

Abstract

Models fit that use sample data disregarding the process of sample selection can distort the analysis, especially in cases where the sampling plan adopted is informative. If the sampling plan requires that every possible sample has a known and non-zero probability of being selected, and if these probabilities of selection are related to the response variable, even after conditioning on the model’s explanatory variables, the sampling plan is informative and it must be considered in the inference. Several educational assessments might be obtained by informative sampling and the Item Response Theory (IRT) model is applied in many of them. However, in general, the fit of the IRT models disregards the possibility of the informativeness of the sample. The purpose of this work is to propose an approach for fitting dichotomous data under two-stage informative sampling, modeled by a two-level hierarchical IRT model. The inference procedure follows the Bayesian approach. Its main motivation is to be applied to educational assessments, which are carried out by samples obtained through complex and possibly informative sampling designs. The formulation of the IRT model to correct the effects of an informative sample on the inference is developed to the sampling plan used in the National System of the Basic Education Evaluation (SAEB). However, any educational evaluation that considers a two-stage informative sampling plan can use this proposed approach. The new methodology was applied to samples selected from the complete dataset obtained from SAEB 2017 edition, with the same sampling plan adopted in SAEB evaluations. In order to check the importance of considering the sampling plan in modelling, the proposed approach was compared with some traditional methodologies that disregard the informativeness of the sample.