  This paper presents a new class of regression models for continuous data
restricted to the interval $(0,1)$, such as rates and proportions. The proposed
class of models assumes a beta distribution for the variable of interest with
regression structures for the mean and dispersion parameters. These structures
consider covariates, unknown regression parameters, and parametric link
functions. Link functions depend on parameters that model the relationship
between the random component and the linear predictors. The symmetric and
assymetric Aranda-Ordaz link functions are considered in details. Depending on
the parameter values, these link functions refer to particular cases of fixed
links such as logit and complementary log-log functions. Joint estimation of
the regression and link function parameters is performed by maximum likelihood.
Closed-form expressions for the score function and Fisher's information matrix
are presented. Aspects of large sample inferences are discussed, and some
diagnostic measures are proposed. A Monte Carlo simulation study is used to
evaluate the finite sample performance of point estimators. Finally, a
practical application that employs real data is presented and discussed.
