Modelos de resposta limitada para regressão e teoria de resposta ao item

Abstract

Some bounded response regression models have been recently proposed in the literature to model rates and proportions. In this way, we initially studied the Beta, Simplex and L-logistic regression models considering a Bayesian estimation of the parameters of the three models using the No-U-Turn sampler (NUTS) algorithm from the implementation via the Stan package. A comparative parameter recovery study is implemented and a performance study of different packages is carried out. Finally, applications were carried out, the first with generated data and the other two with real data about poverty in Peru and in the municipalities of Brazil, respectively, and were presented comparing the performance of the models for the estimation of small and large samples. Furthermore, we propose a new quantile regression model with a bounded response distribution that generalizes the L-logistic distribution. Following a bayesian approach, estimation model comparison criteria and residual analysis are performed as well as a simulation study for prior sensitivity and parameter recovery. An application of the new distribution to model poverty vulnerability in Brazil and a regression analysis with poverty data from Peru is included. Comparison with the L-Logistic and G-Logistic distributions are also performed showing the great flexibility of the new model. Another example of modeling for bounded responses is the time it takes an examinee to perform a computerized test, for example. In this sense, we also propose a model in the hierarchical bayesian context, in order to model the response time (RT) following a bounded distribution and obtain a joint model in combination with the accuracy of the response by considering Bernoulli model and for the precision we consider the Normal Ogive model, from the Item Response Theory (IRT). To model the RT proportion, we initially propose the use of the Beta distribution and perform a Bayesian approach for parameter estimation using the R2jags package. A brief parameter recovery simulation study was developed and the model was applied to a real PISA 2015 computer readout dataset.