  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.
