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

Abstract

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.

Publication
In Statistics Surveys
Justin Petrovich
Justin Petrovich
Associate Professor of Statistics and Business Data Analytics

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