An Application of a Mixed‐Effects Location Scale Model for Analysis of Ecological Momentary Assessment (EMA) Data

Abstract

SummaryFor longitudinal data, mixed models include random subject effects to indicate how subjects influence their responses over 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 (i.e., error variance) and between-subjects (i.e., random-effects variance) variation in the data. In studies using ecological momentary assessment (EMA), up to 30 or 40 observations are often obtained for each subject, and interest frequently centers around changes in the variances, both within and between subjects. In this article, we focus on an adolescent smoking study using EMA where interest is on characterizing changes in mood variation. We describe how covariates can influence the mood variances, and also extend 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.

Orthodontic pain trajectories in adolescents: Between-subject and within-subject variability in pain perception

“…The remaining 115 patients (mean age 14.99, SD ±1.90; males 56, 48.7%; females 59, 51.3%) adhered to the study protocol and provided pain data over the observed time period following orthodontic separator placement. An advantage of mixedeffects models for repeated measures data is that they can handle subject-to-subject variation in the timing of measurements as well as the missing data under the missing at random (MAR) assumption, 10,14 and therefore subjects do not need to provide outcome measurements at exactly the same time points. In our study, subjects were asked to record their pain intensity as close as possible to the scheduled measurement occasions (1, 2, 4, 12 hours etc.).…”

“…Thus, mixed-effects models provide a popular way to not only estimate overall mean relationships, but to additionally quantify and then explain the degree of BS and WS variation in individuals' outcomes over time. 8,9 Recently, Hedeker et al 10,11 extended the standard two-level random-intercept mixedeffects model to additionally model as a function of the covariates both the BS variation in subjects' trajectories about their overall mean trajectory and the WS variation in their observed measurements about their own trajectories. They term their model the "mixed-effects location scale model" where "location" refers to the usual modelling of the mean response, while "scale" refers to the new direct modelling of the BS and WS response variability.…”

On the relation of mean reaction time and intraindividual reaction time variability.

“…Hoffman, 2007)-a highly advantageous option for many interesting research questions. Taking these ideas one step further, recent methodological developments even allow us to model interindividual differences in the amount of intraindividual variability as random effects (in so-called random scale models ;Hedeker, Mermelstein, & Demirtas, 2008).…”

Multilevel growth curve models that incorporate a random coefficient model for the level 1 variance function

“…To this end Hedeker et al 4 consider variance component models where the logarithm of the level 1 variance is a linear function of explanatory variables with an additional simple random effect that can vary across level 2 units and is allowed to correlate with the conventional level 2 random effects describing betweenindividual variation in growth patterns. They show how to obtain maximum likelihood estimates and implement this in the stand-alone MIXREGLS software 6 which is also accessible from within Stata 7 .…”

“…This has been extended 3 to the multivariate case where several measurements are modelled simultaneously. Another extension is to allow the residual, within individual, variation to be modelled as a function of time and other covariates, where the parameters of this model component may be individual-specific and allowed to correlate with other individual random effects 4,5 . The present paper brings together these developments within a single framework and applies the model to data both on adolescent height growth and changes in weight during pregnancy.…”