Specifying Location-Scale Models for Heterogeneous Variances as Multilevel SEMs

Abstract

Standard multilevel models focus on variables that predict the mean while the within-group variability is largely treated as a nuisance. Recent work has shown the advantage of including predictors for both the mean (the location submodel) and the variability (the scale submodel) within a single model. Constrained versions of the model can be fit in standard mixed effect model software, but the most general version with random effects in each of the location and scale submodels has been noted for being difficult to fit and estimate in software. However, the latest release of Mplus includes new capabilities that facilitate fitting the general version of the model as a multilevel structural equation model (SEM). This article introduces the general form of the model that includes location and scale random effects (called the location-scale model) and notes how it can be envisioned as a multilevel SEM. We provide a tutorial with example analyses and Mplus code for the model with two-level cross-sectional data and three-level repeated measures data and discuss how such a model has potential to extend recent developments in organizational science.

“I felt so old this morning.” Short-term variations in subjective age and the role of trait subjective age: Evidence from the ILSE/EMIL ecological momentary assessment data.

“…To test whether age group and trait subjective age-predicted state subjective age variability, we ran location scale models (LSM; McNeish, 2020). LSM allow to enter predictors for the mean (the location model) as well as the within-level variability (the scale model) of a variable in a single multilevel model.…”

The emergence of resilience: Recovery trajectories in sleep functioning after a major stressor.

“…First, we provide a novel operationalisation that synergises concept and method whereby the emergent outcome of 'bounce back resilience' is inferred via temporal changes in within-person variability that support an interpretation of stabilisation in the markers of functioning. Within-person or intra-individual variability in longitudinal data is typically considered a nuisance factor, yet this variation provides rich information about the in/stability of a system that is absent from means alone (Kuppens & Yzerbyt, 2014;Lester et al, 2019;McNeish, 2020). Two people can be equivalent in terms of mean levels of sleep functioning over time, for example, yet differ meaningfully with regard to the magnitude of fluctuations around this average (e.g., low variability versus high variability; see Figure 1).…”

Associations of Wellbeing Levels, Changes, and Within-Person Variability With Late-Life All-Cause Mortality Across 12 Years: Contrasting Hedonic vs. Eudaimonic Wellbeing Among Very Old Adults

“…Third, we considered the residual variance of each individual representing the degree to which the wellbeing measures of individuals fluctuated around the slope trend, thus corresponding to detrended variability of individuals. We used multilevel structural equation models, including a within-person (level 1) location-scale model component to estimate the above-mentioned growth curve parameters as random effects ( McNeish, 2020 ), and a between-person (level 2) regression of time-to-death on these random effects.…”

“…The analyses were run with Mplus (Version 8.5; Muthén and Muthén, 1998-2017 ). To compute the multilevel SEM, Mplus requires to use the “Bayes estimator,” that is, Bayes estimation employing Markov Chain Monte Carlo (MCMC) algorithms (for details see Asparouhov and Muthén, 2010 ; McNeish, 2020 ). Note, thus, that we did not use Bayes estimation from a truly Bayesian perspective, aiming to utilize prior information about the model parameters, but rather took it “as a computational tool for getting estimates that are analogous to what would have been obtained by ML had it been feasible” ( Muthén and Asparouhov, 2012 , p. 314).…”

“… 3 Notably, at present, statistical software packages enabling the estimation of multilevel location scale models ( McNeish, 2020 ) do not allow for widely used survival analyses, such as Cox proportional hazard models at the second level. To check and compare whether our findings would hold in a more conventional survival analysis, we additionally ran two-step analyses, which are, however, compromised by reliability issues.…”