REGRESSION MODELS WITH RESPONSES ON THE UNIT INTERVAL: SPECIFICATION, ESTIMATION AND COMPARISON

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 dierent 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 inated, 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 dene 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 dened 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 dierent