Studying individual differences in predictability With gamma regression and nonlinear multilevel models

Statistical prediction remains an important tool for decisions in a variety of disciplines. An equally important issue is identifying factors that contribute to more or less accurate predictions. The time series literature includes well developed methods for studying predictability and volatility over time. This article develops distribution-appropriate methods for studying individual differences in predictability for settings in psychological research. Specifically, 3 different approaches are discussed for modeling predictability. The 1st is a bivariate measure of predictability discussed previously in the psychology literature, the squared or absolute valued difference between criterion and predictor, which is shown to follow the gamma distribution. The 2nd method extended limitations of previous research and involved understanding predictability in regression models. The 3rd method used nonlinear multilevel models to study predictability in settings where participants are nested within clusters. An application was presented using SAS NLMIXED to understand the predictability of college grade point average by student demographic characteristics. The findings from the application suggest that the 1st-year college performance of English as a second language students were, on average, less predictable whereas females and Whites tended to demonstrate more predictable academic performance than their male or racial/ethnic minority counterparts.