Modelling Interval Data with Random Intercepts: A Beta Regression Approach for Clustered and Longitudinal Structures

Beta regression models are a class of models used frequently to model response variables in the interval (0, 1). Although there are articles in which these models are used to model clustered and longitudinal data, the prediction of random effects is limited, and residual analysis has not been implemented. In this paper, a random intercept beta regression model is proposed for the complete analysis of this type of data structure. We proposed some types of residuals and formulate a methodology to obtain the best prediction of random effects. This model is developed through the parameterisation of beta distribution in terms of the mean and dispersion parameters. A log-likelihood function is approximated by the Gauss–Hermite quadrature to numerically integrate the distribution of random intercepts. A simulation study is used to investigate the performance of the estimation process and the sampling distributions of the residuals.