Explained Variance Measures for Multilevel Models

By David M. LaHuis, Michael J. Hartman, Shotaro Hakoyama, P. Clark. 2014

235 citations recorded by the source corpus.

One challenge in using multilevel models is determining how to report the amount of explained variance. In multilevel models, explained variance can be reported for each level or for the total model. Existing measures have been based primarily on the reduction of variance components across models. However, these measures have not been reported consistently because they have some undesirable properties. The present study is one of the first to evaluate the accuracy of these measures using Monte Carlo simulations. In addition, a measure based on the full partitioning of variance in multilevel models was examined. With the exception of the Level 2 explained variance measure, all other measures performed well across our simulated conditions.

Subfields: Economics and Econometrics, Organizational Behavior and Human Resource Management, Radiological and Ultrasound Technology

View Paper: https://www.semanticscholar.org/paper/f6a3cd90a97db302ab9329c5ff3bad29e9b53cd7

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Citations in the corpus

An R2 statistic for fixed effects in the generalized linear mixed model (2017, background): “[22] discuss several major issues that researchers may encounter when reporting explained variance in mixed models.”
Quantifying explained variance in multilevel models: An integrative framework for defining R-squared measures. (2019, methodology): “Although lists of existing MLM R2 measures proposed by different authors have been compiled (e.g., Jaeger et al., 2017; LaHuis et al., 2014; Orelien & Edwards, 2008; Roberts et al., 2011; Wang & Schaalje, 2009), general analytic relationships and equivalencies among these measures in the population…”
Be smart, play dumb? A transactional perspective on day-specific knowledge hiding, interpersonal conflict, and psychological strain (2021, background): “Day-level specific R 2 (Bryk and Raudenbush, 1992; LaHuis et al., 2014) were .03 for evasive hiding, .04 for playing dumb, .03 for exhaustion, and .10 for negative affect.”
The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded (2016, unknown): “Our descriptions were limited to random-intercept GLMMs, but Johnson [4] has 33 recently extended the methods to random-slope GLMMs, widening the applicability of these 34 statistics (see also, [5, 6]).”
What Predicts Positive Life Events that Influence the Course of Depression? A Longitudinal Examination of Gratitude and Meaning in Life (2017, background): “The variance explained by gratitude was 1.5 % (LaHuis et al. 2014).”
A Within-Person Examination of the Effects of Telework (2014, methodology): “We also calculated a level 1 pseudo-R2 (a more detailed description can be found in LaHuis et al. 2013).”
A Dynamic Model of Entrepreneurial Uncertainty and Business Opportunity Identification: Exploration as a Mediator and Entrepreneurial Self-Efficacy as a Moderator (2017, methodology): “¼ amount of variance explained at the within-person or monthly level by the predictors in the model based on a random-intercept model (LaHuis et al., 2014).”