Modeling individual differences: A case study of the application of system identification for personalizing a physical activity intervention

Background: Control systems engineering methods, particularly, system identification (system ID), offer an idiographic (i.e., person-specific) approach to develop dynamic models of physical activity (PA) that can be used to personalize interventions in a systematic, scalable way. The purpose of this work is to: (1) apply system ID to develop individual dynamical models of PA (steps/day measured using Fitbit Zip) in the context of a goal setting and positive reinforcement intervention informed by Social Cognitive Theory; and (2) compare insights on potential tailoring variables (i.e., predictors expected to influence steps and thus moderate the suggested step goal and points for goal achievement) selected using the idiographic models to those selected via a nomothetic (i.e., aggregated across individuals) approach. Method: A personalized goal setting and positive reinforcement intervention was deployed for 14 weeks. Baseline PA measured in weeks 1–2 was used to inform personalized daily step goals delivered in weeks 3–14. Goals and expected reward points (granted upon goal achievement) were pseudo-randomly assigned using techniques from system ID, with goals ranging from their baseline median steps/day up to 2.5× baseline median steps/day, and points ranging from 100 to 500 (i.e., $0.20–$1.00). Participants completed a series of daily self-report measures. Auto Regressive with eXogenous Input (ARX) modeling and multilevel modeling (MLM) were used as the idiographic and nomothetic approaches, respectively. Results: Participants (N = 20, mean age = 47.25 ± 6.16 years, 90% female) were insufficiently active, overweight (mean BMI = 33.79 ± 6.82 kg/m²) adults. Results from ARX modeling suggest that individuals differ in the factors (e.g., perceived stress, weekday/weekend) that influence their observed steps/day. In contrast, the nomothetic model from MLM suggested that goals and weekday/weekend were the key variables that were predictive of steps. Assuming the ARX models are more personalized, the obtained nomothetic model would have led to the identification of the same predictors for 5 of the 20 participants, suggesting a mismatch of plausible tailoring variables to use for 75% of the sample. Conclusion: The idiographic approach revealed person-specific predictors beyond traditional MLM analyses and unpacked the inherent complexity of PA; namely that people are different and context matters. System ID provides a feasible approach to develop personalized dynamical models of PA and inform person-specific tailoring variable selection for use in adaptive behavioral interventions.