A straightforward approach for coping with unreliability of person means when parsing within-person and between-person effects in longitudinal studies

Abstract

Longitudinal studies enable researchers to distinguish within-person (i.e., time-varying) from between-person (i.e., time invariant) effects by using the person mean to model between-person effects and person-mean centering to model within-person effects using multilevel models (MLM). However, with some exceptions, the person mean tends to be based on a relatively small number of observations available for each participant in longitudinal studies. Unreliability inherent in person means generated with few observations results in downwardly biased between-person and cross-level interaction effect estimates. This manuscript considers a simple, easy-to-implement, post-hoc bias adjustment to correct for attenuation of between-person effects caused by unreliability of the person mean. This correction can be applied directly to estimates obtained from MLM. We illustrate this method using data from a panel study predicting adolescent alcohol involvement from perceived parental monitoring, where parental monitoring was disaggregated into within-person (i.e., person-mean-centered) and between-person (i.e., person-mean) components. We then describe results of a small simulation study that evaluated the performance of the post-hoc adjustment under data conditions that mirrored those of the empirical example. Results suggested that, under a condition in which parameter bias is known to be problematic (i.e., moderate ICCX, small n, presence of a compositional effect), it is preferable to use the bias-adjusted MLM estimates over the unadjusted MLM estimates for between-person and cross-level interaction effects.