Mood Changes Associated with Smoking in Adolescents: An Application of a Mixed-Effects Location Scale Model for Longitudinal Ecological Momentary Assessment (EMA) Data
Hakan Demirtas, University of Illinois at Chicago 
*Donald Hedeker, University of Illinois at Chicago 
Robin Mermelstein, University of Illinois at Chicago 

Keywords: Intensive longitudinal data

For longitudinal data, mixed models include random subject effects to indicate how subjects influence their responses over the repeated assessments. The error variance and the variance of the random effects are usually considered to be homogeneous. These variance terms characterize the within-subjects (error variance) and between-subjects (random-effects variance) variation in the data. In studies using Ecological Momentary Assessment (EMA), up to thirty or forty observations are often obtained for each subject, and interest frequently centers around changes in the variances, both within- and between-subjects. Also, such EMA studies often include several waves of data collection. In this presentation, we focus on an adolescent smoking study using EMA at several measurement waves, where interest is on characterizing changes in mood variation associated with smoking. We describe how covariates can influence the mood variances, and also describe an extension of the standard mixed model by adding a subject-level random effect to the within-subject variance specification. This permits subjects to have influence on the mean, or location, and variability, or (square of the) scale, of their mood responses. Additionally, we allow the location and scale random effects to be correlated. These mixed-effects location scale models have useful applications in many research areas where interest centers on the joint modeling of the mean and variance structure.