Abstract
The use of intensive sampling methods, such as ecological momentary assessment (EMA), is increasingly prominent in medical research. However, inferences from such data are often limited to the subject-specific mean of the outcome and between-subject variance (i.e., random intercept), despite the capability to examine within-subject variance (i.e., random scale) and associations between covariates and subject-specific mean (i.e., random slope). MixWILD (Mixed model analysis With Intensive Longitudinal Data) is statistical software that tests the effects of subject-level parameters (variance and slope) of time-varying variables, specifically in the context of studies using intensive sampling methods, such as ecological momentary assessment. MixWILD combines estimation of a stage 1 mixed-effects location-scale (MELS) model, including estimation of the subject-specific random effects, with a subsequent stage 2 linear or binary/ordinal logistic regression in which values sampled from each subject’s random effect distributions can be used as regressors (and then the results are aggregated across replications). Computations within MixWILD were written in FORTRAN and use maximum likelihood estimation, utilizing both the expectation-maximization (EM) algorithm and a Newton–Raphson solution. The mean and variance of each individual’s random effects used in the sampling are estimated using empirical Bayes equations. This manuscript details the underlying procedures and provides examples illustrating standalone usage and features of MixWILD and its GUI. MixWILD is generalizable to a variety of data collection strategies (i.e., EMA, sensors) as a robust and reproducible method to test predictors of variability in level 1 outcomes and the associations between subject-level parameters (variances and slopes) and level 2 outcomes.
Highlights
Mixed-effects regression models have become a popular method for analysis of longitudinal and clustered (Goldstein, 2011; Raudenbush & Bryk, 2002) data
The model is configured in MixWILD using the following parameters after specifying a data file location and title: 1. Random Location Effects: Here, Intercept and Slope(s) is specified, telling the software to constrain the modeling of effects on between-subject variance, but allow for modeling of multiple random location effects
The stage 2 results table contains the intercept, subject level regressors predicting the subject-level outcome, the effect of the subject-level mean and any interactions on obesity risk, the effect of the within-subject association between weekday/weekend and positive affect and any interactions on obesity risk, the effect of withinsubject variance and any interactions on obesity risk, and the interaction between random intercept and random scale on obesity risk, and any specified three-way interactions
Summary
Mixed-effects regression models (aka hierarchical linear models or multilevel models) have become a popular method for analysis of longitudinal and clustered (Goldstein, 2011; Raudenbush & Bryk, 2002) data. A random subject intercept effect reflects a subject’s mean (or location), whereas a random scale effect reflects a subject’s variability For this example, the stage 2 component is a single-level linear regression model predicting a continuous subject-level outcome using the random subject effects from the stage 1 model as regressors, with the option of. The study seeks to understand whether subjects’ age (a continuous, between-subject, timeinvariant variable) moderates the effect of subjects’ mean (i.e., random intercept) and variance (i.e., random scale) in momentary positive affect in predicting subject-level average hours per day of sedentary behavior, after controlling for sex and day of week. The model is configured in MixWILD using the following parameters after specifying a data file location and title (see Fig. 11): 1. Random Location Effects: Here, Intercept is specified, telling the software to assume only a random subject intercept, but allowing modeling of covariates on between-subject variance
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