MixWILD: A program for examining the effects of variance and slope of time-varying variables in intensive longitudinal data

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.

Joint Modeling of Individual Trajectories, Within-Individual Variability, and a Later Outcome: Systolic Blood Pressure Through Childhood and Left Ventricular Mass in Early Adulthood

“…While fitting joint models involves greater computational burden and complexity compared with a 2-stage approach, the latter is known to introduce bias ( 3 ). Note, though, that a recent methodological development of the 2-stage approach preserves uncertainty in estimates ( 44 ). A 2-stage approach might appear more logical in cases where it is not feasible for the later outcome to influence the earlier longitudinal process, due to fears over allowing the future to cause the past ( 44 , 45 ).…”

“…Note, though, that a recent methodological development of the 2-stage approach preserves uncertainty in estimates ( 44 ). A 2-stage approach might appear more logical in cases where it is not feasible for the later outcome to influence the earlier longitudinal process, due to fears over allowing the future to cause the past ( 44 , 45 ). The joint modeling framework, however, uses future measurements to improve the model for the past measurements, rather than to cause the past measurements.…”

Affective variability and childhood abuse increase the risk for nonsuicidal self‐injury following psychiatric hospitalization

“…Before conducting the main analyses, we examined whether patterns of missingness were associated with demographic characteristics. Data management was conducted using R (R Core Team, 2019), and main analyses were conducted using MixWILD (Dzubur et al., 2020; Hedeker & Nordgren, 2013). Analyses were conducted using a two‐stage approach.…”

“…To examine our first objective (i.e., the impact of childhood abuse on affect intensity and variability), we conducted a series of mixed‐effects LSMs. The LSM is an extension of random‐intercept mixed‐effects regression in which log‐linear submodels are included to allow independent predictors of both the between‐ and within‐person variance estimates (Dzubur et al., 2020; Hedeker et al., 2008; Nordgren et al., 2020). In the LSM, the random location (i.e., intercept) reflects the degree to which a participant deviates from the population mean and the random scale (i.e., participant‐specific, within‐person variance term) reflects the degree to which a participant deviates from their own means.…”

“…Ceiling and floor effects are commonly observed when more variability exists in the middle range of the scale in contrast to a more restricted variability at the upper and lower extremes. Finally, to aid model convergence, individuals with no variability in affect were excluded as this can cause estimation issues concerning the random scale (Dzubur et al., 2020).…”