Scalar-on-Function Regression for Predicting Distal Outcomes from Intensively Gathered Longitudinal Data: Interpretability for Applied Scientists


Researchers are sometimes interested in predicting a distal or external outcome (such as smoking cessation at follow-up) from the trajectory of an intensively recorded longitudinal variable (such as urge to smoke). This can be done in a semiparametric way via scalar-on-function regression. However, the resulting fitted coefficient regression function requires special care for correct interpretation, as it represents the joint relationship of time points to the outcome, rather than a marginal or cross-sectional relationship. We provide practical guidelines, based on experience with scientific applications, for helping practitioners interpret their results and illustrate these ideas using data from a smoking cessation study.

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Justin Petrovich
Justin Petrovich
Assistant Professor of Statistics and Business Data Analytics

My research interests include functional and longitudinal data analysis, applied statistics, and statistics education.