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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. [ABSTRACT FROM AUTHOR]

We propose a multivariate regression model to handle multiple continuous bounded outcomes. We adopted the maximum likelihood approach for parameter estimation and inference. The model is specified by the product of univariate probability distributions and the correlation between the response variables is obtained through the correlation matrix of the random intercepts. For modeling continuous bounded variables on the interval (0,1) we considered the beta and unit gamma distributions. The main advantage of the proposed model is that we can easily combine different marginal distributions for the response variable vector. The computational implementation is performed using Template Model Builder, which combines the Laplace approximation with automatic differentiation. Therefore, the proposed approach allows us to estimate the model parameters quickly and efficiently. We conducted a simulation study to evaluate the computational implementation and the properties of the maximum likelihood estimators under different scenarios. Moreover, we investigate the impact of distribution misspecification in the proposed model. Our model was motivated by a data set with multiple continuous bounded outcomes, which refer to the body fat percentage measured at five regions of the body. Simulation studies and data analysis showed that the proposed model provides a general and rich framework to deal with multiple continuous bounded outcomes. [ABSTRACT FROM AUTHOR]