Beta rectangular regression models to longitudinal data

Abstract

In this paper, we propose a new approach for modeling repeated measures restricted to the interval $(0,1)$ (or $(\mathit{a},\mathit{b})$, with $\mathit{a}<\mathit{b}$ known real numbers). More specifically, we developed Generalized Estimating Equations, considering beta rectangular marginal distributions, which is more robust than the usual beta distribution, against the presence of extreme observations. Diagnostic tools, including local influence analysis, were also developed. A simulation study was performed, indicating that our estimation algorithm is efficient, in terms of parameter recovery. The results also suggest that our methodology outperformed the usual beta model, for the most of the considered scenarios, indicating an interesting advantage on the estimation of the dispersion parameter. Furthermore, the developed methodology was illustrated through a real data analysis, concerning to an ophthalmic study.