A better lemon-squeezer? Maximum likelihood regression with beta-distributed dependent variables

Uncorrectable skew and heteroscedasticity are the “lemons” of social psychological data. Nonetheless, there are plenty of variables whose distributions naturally exhibit these properties. Fortoo long researchers have been forced to ignore or transform away what could be important aspects of their data. For variables whose scales have a lowerand upper bound, help is at hand via the beta distribution, which is very flexible and models skew quite well. We provide maximum-likelihood regression models assuming the dependent variable is conditionally beta-distributed, not Gaussian. Our approach allows researchers to model both means (location) and variances (dispersion) with their own distinct sets of predictors (either continuous or categorical), thereby modelling heteroscedasticity. The location submodel is analogous to logistic regression, while the dispersion submodel is log-linear. Examples from real data-sets demonstrate that these models can handle any experimental design or correlational study. User-friendly syntax is available in SAS, SPSS, and R/SPlus.TTRU