A three-level mixed model to account for the correlation at both the between-day and the within-day level for ecological
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A three‑level mixed model to account for the correlation at both the between‑day and the within‑day level for ecological momentary assessments Qianheng Ma1 · Robin Mermelstein2 · Donald Hedeker1 Received: 5 May 2020 / Revised: 17 August 2020 / Accepted: 5 September 2020 / Published online: 23 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Ecological Momentary Assessment (EMA) studies aim to explore the interaction between subjects’ psychological states and real environmental factors. During the EMA studies, participants can receive prompted assessments intensively across days and within each day, which results in three-level longitudinal data, e.g., subject-level (level-3), day-level nested in subject (level-2) and assessment-level nested in each day (level-1). Those three-level data may exhibit complex longitudinal correlation structure but ignoring or mis-specifying the within-subject correlation structure can lead to bias on the estimation of the key effects and the intraclass correlation. Given the three-level EMA data and the time stamps of the responses, we proposed a linear mixed effects model with random effects at each level. In this model, we accounted for level-2 autocorrelation and level-1 autocorrelation and showed how structural information from the three-level data improved the fit of the model. With real time stamps of the assessments, we also provided a useful extension of this proposed model to deal with the issue of irregular-spacing in EMA assessments. Keywords EMA · Intensive multilevel longitudinal data · Mixed effect model · AR(1) · Irregular-spaced assessments
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s1074 2-020-00220-w) contains supplementary material, which is available to authorized users. * Qianheng Ma [email protected] Robin Mermelstein [email protected] Donald Hedeker [email protected] 1
Department of Public Health Sciences, University of Chicago, Chicago, USA
2
Institute for Health Research and Policy, University of Illinois at Chicago, Chicago, USA
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Vol.:(0123456789)
248
Health Services and Outcomes Research Methodology (2020) 20:247–264
1 Introduction The Ecological Momentary Assessment (EMA) design (Shiffman et al. 2008) is helpful to explore the interaction between subjects’ psychological states and real environmental factors. In those EMA studies, psychologically or behaviorally related questionnaires are prompted to participants via hand-held devices multiple times within a day as well as across days. In other words, the collected EMA data are usually three-level data where assessments at level 1 are nested within days at level 2, and days are nested within subjects at level 3. Unlike other conventional longitudinal data where the interval between consecutive assessments is usually much longer (e.g., every six months), EMA assessments which are prompted in high frequency are usually longitudinally closely related to one another so that researchers m
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