Unit gamma regression models for correlated bounded data

Experiments with repeated measures are the ones where more than one observation per subject is available. To model of such experiments, dependency within subjects needs to be taken into consideration. In cases where the variable of interest is bounded in (a, b) with a < b known reals, there are few proposals to model correlated bounded data most part being based on Beta, Simplex and Unit gamma distributions. In particular, for marginal modeling of the mean and precision/dispersion, Simplex and Beta models based on Generalized Estimating Equations (GEE) are used. In this paper, to take account of possible within-subject dependence using the GEE approach, we proposed an Unit Gamma regression model used to modeling bounded data in a unit interval. In this paper, we developed residuals and influence diagnostic tools to the Simplex and Unit Gamma models for correlated bounded data. Furthermore, To assess the finite-sample performance of the proposed estimators, we conducted a Monte Carlo simulation study. The methodology is illustrated with the analysis of a real data set. An R package was developed for all the new methodology described in this paper.