Modeling Inertia in Intensive Longitudinal Count Data: A Multilevel Log-Linear Poisson Autoregressive Approach for Behavioral Processes

Inertia, widely studied in psychological research for its implications for psychologicalhealth and emotion regulation, is typically operationalized as the lag-1 autoregressiveeffect in time series linear models. The recent proliferation of intensivelongitudinal designs, such as ecological momentary assessment (EMA) and daily diarymethods facilitated by mobile technology, enables researchers to capture repeated,real-time information about contextual, physical, and emotional factors, allowing forthe study of inertia across diverse psychological contexts. However, the utilizationof raw count data—a common practice in recording time-sensitive events or behaviorssuch as drinking episodes or mood fluctuations—may introduce unintended bias,yielding suboptimal estimates. Moreover, the conceptualization of inertia with countintensive longitudinal data (ILD) remains understudied in existing methodological literature.Building upon time series methodology, we provide a novel framework for exploringthis concept in detail, demonstrating how the relationship between inertia andautocorrelation in count data can deviate from their relationship in linear models, andexamining connections with commonly used temporal indices in psychology. Throughcomprehensive simulation studies and an empirical alcohol use disorder study, we: (1)evaluate the validity of existing methods for estimating autoregressive processes withcount ILD; (2) propose an alternative approach for conceptualizing and quantifyinginertia in count ILD; and (3) offer practical guidance for applied researchers on interpretinginertia in count data contexts. Finally, we discuss broader implications ofthe proposed methodology, including how it can inform more effective interventiondesign in psychological studies, and outline future research directions.