Modelo de regressão L-logística com perspectiva frequentista

Abstract

In this work we study the L-logistic distribution proposed in Paz et al. (2016) and its respective regression model for modeling variables in a limited range, generally (0, 1), such as rates and proportions. As far as the modeling of this type of variables is concerned, a significant percentage is found in the literature for Beta and Simplex models. With the objective of diversifying the literature, this work makes its inferences through of the estimation method by maximum likelihood (ML) to contribute to the frequentist method, considering that the work done in Paz et al. (2016) presents only the Bayesian method. The method of inference is accomplished through the combination of evolutionary algorithms (Genetic Algorithm and Differential Evolution) to obtain the point estimates (dispensing the use of derivatives in the process) and resampling methods (Jackknife and Bootstrap) to obtain the estimates of the standard error and confidence intervals. Simulations are performed to illustrate the combination of techniques and to prove their efficiency. Then, the potential of the model is demonstrated through two applications in real data, in which a better performance of the L-logistic regression model is verified in relation to the Beta and Simplex regression models (in terms of goodness of fit measures and a measure to influential points).