Regression models are widely used on a diversity of application areas to describe associations between explanatory and response variables. The initially and frequently adopted Gaussian linear model was gradually extended to accommodate different kinds of response variables. These models were latter described as particular cases of the generalized linear models (GLM). The GLM family allows for a diversity of formats for the response variable and functions linking the parameters of the distribution to a linear predictor. This model structure became a benchmark for several further extensions and developments in statistical modelling such as generalized additive, overdispersed, zero inflated, among other models. Response variables with values restricted to an interval, often (0, 1), are usual in social sciences, agronomy, psychometrics among other areas. Beta or Simplex distributions are often used although other options are mentioned in the literature. In this paper, a generic structure is used to define a set of regression models for restricted response variables, not only including the usually assumed formats but allowing for a wider range of models. Individual models are defined by choosing three components: the probability distribution for the response; the function linking the parameter of the distribution of choice with the linear predictor; and the transformation function for the response. We report results of the analysis of four different datasets considering Beta, Simplex, Kumaraswamy and Gaussian distributions. For the link and transformation functions the logit, probit, complementary log-log, log-log, Cauchit and Aranda-Ordaz are considered. Likelihood based analysis for model fitting, comparison and model choice are carried out on a unified way and a computer code is made available. Results show there is no prominent model within this class highlighting the importance of investigating a wide range of models for each problem at hand.