Regression analysis of variates observed on (0, 1): percentages, proportions and fractions

Many types of studies examine the influence of selected variables on the conditional expectation of a proportion or vector of proportions, for example, market shares, rock composition, and so on. We identify four distributional categories into which such data can be put, and focus on regression models for the first category, for proportions observed on the open interval (0, 1). For these data, we identify different specifications used in prior research and compare these specifications using two common samples and specifications of the regressors. Based upon our analysis, we recommend that researchers use either a parametric regression model based upon the beta distribution or a quasi-likelihood regression model developed by Papke and Wooldridge (1997) for these data. Concerning the choice between these two regression models, we recommend that researchers use the parametric regression model unless their sample size is large enough to justify the asymptotic arguments underlying the quasi-likelihood approach.