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Bounded response variables are common in many applications where the responses are percentages, proportions, or rates. New regression models have been proposed recently to model the relationship among one or more covariates and the conditional mean of a response variable based on the beta distribution or a mixture of beta distributions. However, when we are interested in knowing how covariates impact different levels of the response variable, quantile regression models play an important role. A new quantile parametric mixed regression model for bounded response variables is presented by considering the distribution introduced by [27]. A Bayesian approach is adopted for inference using Markov Chain Monte Carlo (MCMC) methods. Model comparison criteria are also discussed. The inferential methods can be easily programmed and then easily used for data modeling. Results from a simulation study are reported showing the good performance of the proposed inferential methods. Furthermore, results from data analyses using regression models with fixed and mixed effects are given. Specifically, we show that the quantile parametric model proposed here is an alternative and complementary modeling tool for bounded response variables such as the poverty index in Brazilian municipalities, which is linked to the Gini coefficient and the human development index.

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In biomedical studies, the analysis of longitudinal data based on Gaussian assumptions is common practice. Nevertheless, more often than not, the observed responses are naturally skewed, rendering the use of symmetric mixed effects models inadequate. In addition, it is also common in clinical assays that the patient's responses are subject to some upper and/or lower quantification limit, depending on the diagnostic assays used for their detection. Furthermore, responses may also often present a nonlinear relation with some covariates, such as time. To address the aforementioned three issues, we consider a Bayesian semiparametric longitudinal censored model based on a combination of splines, wavelets, and the skew-normal distribution. Specifically, we focus on the use of splines to approximate the general mean, wavelets for modeling the individual subject trajectories, and on the skew-normal distribution for modeling the random effects. The newly developed method is illustrated through simulated data and real data concerning AIDS/HIV viral loads.