A Three-Level Mixed Model to Account for the Correlation at both the Between-Day and the Within-Day Level for Ecological Momentary Assessments.

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.