Modeling Change in Skewed Variables Using Mixed Beta Regression Models

Abstract

The general linear model relies on the assumptions of independent and normally distributed residuals with constant variance. If these assumptions are not met, beta regression models represent a viable alternative to model variables that show skewness and heteroscedasticity. In this study, the beta regression model is extended to include random effects. Such a mixed beta regression model can account for the data dependency present in longitudinal data by allowing for participant-specific effects. The mixed beta regression model is illustrated using longitudinal data on complex choice reaction times. Results show that a model with fixed age and missingness effects as well as random intercept and age slope effects fitted the data best. Importantly, it fitted the data much better than a linear mixed model did. Alternatives to the mixed beta regression model and potential applications are described in the discussion.