Statistical Models for Multilevel Skewed Physical Activity Data in Health Research and Behavioral Medicine

Objective:Researchers who study physical activity often use outcome variables that have a lower bound of zero and are positively skewed (e.g., minutes of physical activity in a day). Researchers also often use statistical methods that assume the outcome is normally distributed or transform the outcome as an attempt to make it more normal, both of which can be problematic. In this article, the authors describe multilevel 2-part models that use a mixture of logistic regression-to predict whether a person was active-and gamma regression-to predict amount of activity if there was activity. Method:The authors contrast the 2-part models to a linear multilevel model using data from a longitudinal study of physical activity (N = 113; 2,305 observations). The dependent variable was minutes of moderate-to-vigorous activity in a day and the predictor variables were day, satisfaction, and gender. Results:The 2-part models outperform the linear model and provide researchers critical information that is conceptually relevant, such as distinguishing between predictors of whether activity occurred and of how much activity occurred. Conclusions:Two-part models represent a flexible and useful addition to the analysis repertoire of health researchers. To assist researchers in learning these methods, the online supplemental materials provide additional technical information as well as annotated computer code for estimating these models.