We propose the unit gamma mixed regression model to deal with continuous bounded variables in the context of repeated measures and clustered data. The proposed model is based on the class of generalized linear mixed models and parameter estimates are obtained based on the maximum likelihood method. The computational implementation combines automatic differentiation and the Laplace approximation (via Template Model Builder/C++) to compute the derivatives of the log-likelihood function with respect to fixed and random effects parameters. We carry out extensive simulations to check the computational implementation and to verify the properties of the maximum likelihood estimators. Our results suggest that the proposed maximum likelihood approach provides unbiased and consistent estimators for all model parameters. The proposed model was motivated by two data sets. The first concerns the body fat percentage, where the goal was to investigate the effect of covariates which were taken in the same subject. The second data set refers to a water quality index data, where the main interest was to evaluate the effect of dams on the water quality measured on power plant reservoirs. The data sets and R code are provided as supplementary material.

我们提出单位伽玛混合回归模型来处理重复测量和聚类数据背景下的连续有界变量。所提出的模型基于广义线性混合模型类，参数估计是基于最大似然法获得的。计算实现结合了自动微分和拉普拉斯近似（通过模板模型生成器/C++）来计算对数似然函数关于固定和随机效应参数的导数。我们进行了广泛的模拟来检查计算实现并验证最大似然估计的属性。我们的结果表明，所提出的最大似然法为所有模型参数提供了无偏且一致的估计量。所提出的模型受到两个数据集的启发。第一个涉及体脂百分比，其目标是研究在同一受试者中采用的协变量的影响。第二个数据集是指水质指数数据，主要目的是评估水坝对电厂水库水质的影响。数据集和 R 代码作为补充材料提供。