A potentially useful distribution model for dietary intake data

A Mixed-Effects Location Scale Model for Dyadic Interactions

We present a mixed-effects location scale model (MELSM) for examining the daily dynamics of affect in dyads. The MELSM includes person and time-varying variables to predict the location, or individual means, and the scale, or within-person variances. It also incorporates a submodel to account for between-person variances. The dyadic specification can accommodate individual and partner effects in both the location and the scale components, and allows random effects for all location and scale parameters. All covariances among the random effects, within and across the location and the scale are also estimated. These covariances offer new insights into the interplay of individual mean structures, intra-individual variability, and the influence of partner effects on such factors. To illustrate the model, we use data from 274 couples who provided daily ratings on their positive and negative emotions toward their relationship - up to 90 consecutive days. The model is fit using Hamiltonian Monte Carlo methods, and includes subsets of predictors in order to demonstrate the flexibility of this approach. We conclude with a discussion on the usefulness and the limitations of the MELSM for dyadic research.

A three-level mixed-effects location scale model with an application to ecological momentary assessment data

In studies using ecological momentary assessment (EMA), or other intensive longitudinal data collection methods, interest frequently centers on changes in the variances, both within-subjects and between-subjects. For this, Hedeker et al. (Biometrics 2008; 64: 627-634) developed an extended two-level mixed-effects model that treats observations as being nested within subjects and allows covariates to influence both the within-subjects and between-subjects variance, beyond their influence on means. However, in EMA studies, subjects often provide many responses within and across days. To account for the possible systematic day-to-day variation, we developed a more flexible three-level mixed-effects location scale model that treats observations within days within subjects, and allows covariates to influence the variance at the subject, day, and observation level (over and above their usual effects on means) using a log-linear representation throughout. We provide details of a maximum likelihood solution and demonstrate how SAS PROC NLMIXED can be used to achieve maximum likelihood estimates in an alternative parameterization of our proposed three-level model. The accuracy of this approach using NLMIXED was verified by a series of simulation studies. Data from an adolescent mood study using EMA were analyzed to demonstrate this approach. The analyses clearly show the benefit of the proposed three-level model over the existing two-level approach. The proposed model has useful applications in many studies with three-level structures where interest centers on the joint modeling of the mean and variance structure.

Modeling Individual Differences in Within-Person Variation of Negative and Positive Affect in a Mixed Effects Location Scale Model Using BUGS/JAGS

A mixed effects location scale model was used to model and explain individual differences in within-person variability of negative and positive affect across 7 days (N=178) within a measurement burst design. The data come from undergraduate university students and are pooled from a study that was repeated at two consecutive years. Individual differences in level and change in mood was modeled with a random intercept and random slope where the residual within-person variability was allowed to vary across participants. Additionally changes in within-person variability were explained by the inclusion of a time-varying predictor indicating the severity of daily stressors. This model accounted for 2 location and 2 scale effects and provided evidence that individuals who reported higher severity in daily stressors also exhibited greater variability in affect-but only for participants who showed low overall affect variability and who reported low average negative affect. Those who were more variable in their affect reports overall were less reactive to daily stressors in the sense that their high levels of affect variability remained high. We describe the utility of this model for further research on individual variation and change.

Modeling Within-Person Variance in Reaction Time Data of Older Adults

In order to model within-person (WP) variance in a reaction time task, we applied a mixed location scale model using 335 participants from the second wave of the Zurich Longitudinal Study on Cognitive Aging. The age of the respondents and the performance in another reaction time task were used to explain individual differences in the WP variance. To account for larger variances due to slower reaction times, we also used the average of the predicted individual reaction time (RT) as a predictor for the WP variability. Here, the WP variability was a function of the mean. At the same time, older participants were more variable and those with better performance in another RT task were more consistent in their responses.

An application of a mixed-effects location scale model for analysis of Ecological Momentary Assessment (EMA) data

For 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.