Paulo Justiniano

Bio: Paulo Justiniano is an academic researcher. The author has contributed to research in topics: Binomial regression & Generalized additive model for location, scale and shape. The author has an hindex of 1, co-authored 1 publications receiving 9 citations.

Regression models with responses on the unit interval: specification, estimation and comparison

Abstract: Regression models are widely used on a diversity of application areas to describe associations between explanatory and response variables. The initially and frequently adopted Gaussian linear model was gradually extended to accommodate dierent kinds of response variables. These models were latter described as particular cases of the generalized linear models (GLM). The GLM family allows for a diversity of formats for the response variable and functions linking the parameters of the distribution to a linear predictor. This model structure became a benchmark for several further extensions and developments in statistical modelling such as generalized additive, overdispersed, zero inated, among other models. Response variables with values restricted to an interval, often (0; 1), are usual in social sciences, agronomy, psychometrics among other areas. Beta or Simplex distributions are often used although other options are mentioned in the literature. In this paper, a generic structure is used to dene a set of regression models for restricted response variables, not only including the usually assumed formats but allowing for a wider range of models. Individual models are dened by choosing three components: the probability distribution for the response; the function linking the parameter of the distribution of choice with the linear predictor; and the transformation function for the response. We report results of the analysis of four dierent

Some New Facts about the Unit-Rayleigh Distribution with Applications

Abstract: The unit-Rayleigh distribution is a one-parameter distribution with support on the unit interval. It is defined as the so-called unit-Weibull distribution with a shape parameter equal to two. As a particular case among others, it seems that it has not been given special attention. This paper shows that the unit-Rayleigh distribution is much more interesting than it might at first glance, revealing closed-form expressions of important functions, and new desirable properties for application purposes. More precisely, on the theoretical level, we contribute to the following aspects: (i) we bring new characteristics on the form analysis of its main probabilistic and reliability functions, and show that the possible mode has a simple analytical expression, (ii) we prove new stochastic ordering results, (iii) we expose closed-form expressions of the incomplete and probability weighted moments at the basis of various probability functions and measures, (iv) we investigate distributional properties of the order statistics, (v) we show that the reliability coefficient can have a simple ratio expression, (vi) we provide a tractable expansion for the Tsallis entropy and (vii) we propose some bivariate unit-Rayleigh distributions. On a practical level, we show that the maximum likelihood estimate has a quite simple closed-form. Three data sets are analyzed and adjusted, revealing that the unit-Rayleigh distribution can be a better alternative to standard one-parameter unit distributions, such as the one-parameter Kumaraswamy, Topp–Leone, one-parameter beta, power and transmuted distributions.

Flexible quasi-beta regression models for continuous bounded data:

Abstract: We propose a flexible class of regression models for continuous bounded data based on second-moment assumptions The mean structure is modelled by means of a link function and a linear predictor, w

Quasi-beta Longitudinal Regression Model Applied to Water Quality Index Data

Abstract: We propose a new class of regression models to deal with longitudinal continuous bounded data. The model is specified using second-moment assumptions, and we employ an estimating function approach for parameter estimation and inference. The main advantage of the proposed approach is that it does not need to assume a multivariate probability distribution for the response vector. The fitting procedure is easily implemented using a simple and efficient Newton scoring algorithm. Thus, the quasi-beta longitudinal regression model can easily handle data in the unit interval, including exact zeros and ones. The covariance structure is defined in terms of a matrix linear predictor composed by known matrices. A simulation study was conducted to check the properties of the estimating function estimators of the regression and dispersion parameter estimators. The NORTA algorithm (NORmal To Anything) was used to simulate correlated beta random variables. The results of this simulation study showed that the estimators are consistent and unbiased for large samples. The model is motivated by a data set concerning the water quality index, whose goal is to investigate the effect of dams on the water quality index measured on power plant reservoirs. Furthermore, diagnostic techniques were adapted to the proposed models, such as DFFITS, DFBETAS, Cook’s distance and half-normal plots with simulated envelope. The R code and data set are available in the supplementary material.

Bayesian analysis for a class of beta mixed models

Abstract: Generalized linear mixed models (GLMMs) encompass large class of statistical models, with a vast range of applications areas. GLMMs extend the linear mixed models allowing for dierent types of response variable. Three most common data types are continuous, counts and binary and standard distributions for these types of response variables are Gaussian, Poisson and binomial, respectively. Despite that exibility, there are situations where the response variable is continuous, but bounded, such as rates, percentages, indexes and proportions. In such situations the usual GLMMs are not adequate because bounds are ignored and the beta distribution can be used. Likelihood and Bayesian inference for beta mixed models are not straightforward demanding a computational overhead. Recently, a new algorithm for Bayesian inference called INLA (Integrated Nested Laplace Approximation) was proposed. INLA allows computation of many Bayesian GLMMs in a reasonable amount time allowing extensive comparison among models. We explore Bayesian inference for beta mixed models by INLA. We discuss the choice of prior distributions, sensitivity analysis and model selection measures through a real data set. The results obtained from INLA are compared with those obtained by an MCMC algorithm and likelihood analysis. We analyze data from an study on a life quality index of industry workers collected according to a hierarchical sampling scheme. Results show that the INLA approach is suitable and faster to t the proposed beta mixed models producing results similar to alternative algorithms and with easier handling of modeling alternatives. Sensitivity analysis, measures of goodness of t and model choice are discussed.