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Modeling Multiple Wave Ecological Momentary Assessment (EMA) data with a Mixed-Effects Location Scale Model.

*Chi C Cho, Aurora Research Institute 
Donald Hedeker, University of Illinois at Chicago 

Keywords: Heteroscedasticity, Variance Modeling, Log-linear variance, Complex variation, Multilevel, EMA, Multiple Wave

For traditional longitudinal data, mixed-effects model with only random subject effects to describe how subjects influence their response over repeated measurements may be sufficient and the assumption of homogeneous error variance (within-subject) and random-effects variance (between-subject) may be appropriate. However, with intensive longitudinal data and studies using ecological momentary assessments (EMA), where there are multiple data collection waves for the same study subjects and up to 30 or 40 observations are often collected from each subject for each data collection wave, the variance homogeneity assumption may not be appropriate. Furthermore, the change in both the within and between subject variances may be of primary interest. We propose an extension to the mixed effects location scale model by introducing a subject level random trend effect to the within-subject variance specification. This model is able to capture the subjects’ personal influence on their mean location at initial data collection wave, mean trend across the waves, variability at the initial wave, and linear trend in the variation across the wave on the response. Additionally, we allow all the location and scale random effects to be correlated. With the increase popularity of EMA studies with multiple data collection waves and the research interest centering on jointly modeling mean and variance structures, this extension to the mixed-effects location scale model will be a useful addition to the analytical tool box.