Tatiene Correia de Souza

1. The beta prime (BP) distribution, also known as the inverse beta distribution or beta distribution of the second kind, is an absolutely continuous probability distribution with support on the po...

The beta prime regression model proposed by Bourguignon, Santos-Neto, and de Castro is an alternative to the generalized linear models and useful to model positive asymmetric data. In this paper, we propose two general misspecification tests based on the RESET test for beta prime regression models with varying precision. In the first test, we add the testing variable in the mean submodel, whereas the second test focuses on adding the testing variables in all submodels. We conduct an extensive Monte Carlo simulation study to evaluate the performance of the proposed tests in finite sample size in terms of their sizes and powers, thus obtaining information about the best combination of test statistics and testing variables to perform the proposed tests. We also present and discuss two empirical applications to show the applicability and importance of the proposed tests.

This paper provides a general framework for controlling quality characteristics related to control variables and limited to the intervals (0, 1], [0, 1), or [0, 1]. The proposed control chart is based on the inflated beta regression model considering a reparametrization of the inflated beta distribution indexed by the response mean, which is useful for modeling fractions and proportions. The contribution of the paper is twofold. First, we extend the inflated beta regression model by allowing a regression structure for the precision parameter. We also present closed-form expressions for the score vector and Fisher’s information matrix. Second, based on the proposed regression model, we introduce a new model-based control chart. The control limits are obtained considering the estimates of the inflated beta regression model parameters. We conduct a Monte Carlo simulation study to evaluate the performance of the proposed regression model estimators, and the performance of the proposed control chart is evaluated in terms of run length distribution. Finally, we present and discuss an empirical application to show the applicability of the proposed regression control chart.

Este artigo tem por objetivo identificar os fatores que influenciam a eficiência na aplicação dos recursos destinados à Atenção Básica nos municípios brasileiros. Para isso, utilizou-se o modelo de regressão beta inflacionado, uma vez que a variável dependente apresenta valores no intervalo (0,1]. De acordo com os resultados, o índice Firjan de desenvolvimento municipal na saúde e serviços de saneamento básico são fatores que influenciam positivamente a eficiência média na Atenção Básica de um município. Por outro lado, o gasto per capita de um município, em Atenção Básica, exerce efeito negativo na eficiência média.