Multivariate quasi-beta regression models for continuous bounded data

Abstract

We propose a multivariate regression model to deal with multiple continuous bounded data. The proposed model is based on second-moment assumptions, only. We adopted the quasi-score and Pearson estimating functions for estimation of the regression and dispersion parameters, respectively. Thus, the proposed approach does not require a multivariate probability distribution for the variable response vector. The multivariate quasi-beta regression model can easily handle multiple continuous bounded outcomes taking into account the correlation between the response variables. Furthermore, the model allows us to analyze continuous bounded data on the interval [0, 1], including zeros and/or ones. Simulation studies were conducted to investigate the behavior of the NORmal To Anything (NORTA) algorithm and to check the properties of the estimating function estimators to deal with multiple correlated response variables generated from marginal beta distributions. The model was motivated by a data set concerning the body fat percentage, which was measured at five regions of the body and represent the response variables. We analyze each response variable separately and compare it with the fit of the multivariate proposed model. The multivariate quasi-beta regression model provides better fit than its univariate counterparts, as well as allows us to measure the correlation between response variables. Finally, we adapted diagnostic tools to the proposed model. In the supplementary material, we provide the data set and R code.

Keywords: NORTA algorithm; correlated data; estimating functions; multiple continuous bounded outcomes; simulation study; unit interval.