Likelihood analysis for a class of beta mixed models

Abstract: Beta regression models are a suitable choice for continuous response variables on the unity interval. Random effects add further flexibility to the models and accommodate data structures such as hierarchical, repeated measures and longitudinal, which typically induce extra variability and/or dependence. Closed expressions cannot be obtained for parameter estimation and numerical methods are required and possibly combined with sampling algorithms. We focus on likelihood inference and related algorithms for the analysis of beta mixed models motivated by two real problems with grouped data structures. The first is a study on a life quality index of industry workers with data collected according to an hierarchical sampling scheme. The second is a study with a nested and longitudinal data structure assessing the impact of hydroelectric power plants upon measures of water quality indexes up, downstream and at the reservoirs of the dammed rivers. Relevant scientific hypothesis are investigated by comparing alternative models. The analysis uses different algorithms including data-cloning, an alternative to numerical approximations which also assess identifiability. Confidence intervals based on profiled likelihoods are compared to those obtained by asymptotic quadratic approximations, showing relevant differences for parameters related to the random effects.