Detecting influential subjects in intensive longitudinal data using mixed-effects location scale models

Abstract

Background: Collection of intensive longitudinal health outcomes allows joint modeling of their mean (location) and variability (scale). Focusing on the location of the outcome, measures to detect influential subjects in longitudinal data using standard mixed-effects regression models (MRMs) have been widely discussed. However, no existing approach enables the detection of subjects that heavily influence the scale of the outcome.

Methods: We propose applying mixed-effects location scale (MELS) modeling combined with commonly used influence measures such as Cook's distance and DFBETAS to fill this gap. In this paper, we provide a framework for researchers to follow when trying to detect influential subjects for both the scale and location of the outcome. The framework allows detailed examination of each subject's influence on model fit as well as point estimates and precision of coefficients in different components of a MELS model.

Results: We simulated two common scenarios in longitudinal healthcare studies and found that influence measures in our framework successfully capture influential subjects over 99% of the time. We also re-analyzed data from a health behavior study and found 4 particularly influential subjects, among which two cannot be detected by influence analyses via regular MRMs.

Conclusion: The proposed framework can help researchers detect influential subject(s) that will be otherwise overlooked by influential analysis using regular MRMs and analyze all data in one model despite influential subjects.

Keywords: Cook’s distance; Influential data; Intensive longitudinal data; Mixed-effects location scale model; Variance modeling.