The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
An R2statistic for fixed effects in the generalized linear mixed model
Abstract
Measuring the proportion of variance explained (R2) by a statistical model and the relative importance of specific predictors (semi-partial R2) can be essential considerations when building a parsimonious statistical model. The R2 statistic is a familiar summary of goodness-of-fit for normal linear models and has been extended in various ways to more general models. In particular, the generalized linear mixed model (GLMM) extends the normal linear model and is used to analyze correlated (hierarchical), non-normal data structures. Although various R2 statistics have been proposed, there is no consensus in statistical literature for the most sensible definition of R2 in this context. This research aims to build upon existing knowledge and definitions of R2 and to concisely define the statistic for the GLMM. Here, we derive a model and semi-partial R2 statistic for fixed (population) effects in the GLMM by utilizing the penalized quasi-likelihood estimation method based on linearization. We show that our proposed R2 statistic generalizes the widely used marginal R2 statistic introduced by Nakagawa and Schielzeth, demonstrate our statistics capability in model selection, show the utility of semi-partial R2 statistics in longitudinal data analysis, and provide software that computes the proposed R2 statistic along with semi-partial R2 for individual fixed effects. The software provided is adapted for both SAS and R programming languages.
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Cites
A general and simple method for obtaining R 2 from generalized linear mixed‐effects models
Nakagawa, S., & Schielzeth, H. (2013) · Methods in Ecology and Evolution · doi:10.1111/j.2041-210x.2012.00261.x · Cited by 10,356
Bayesian Measures of Explained Variance and Pooling in Multilevel (Hierarchical) Models
Gelman, A., & Pardoe, I. (2006) · Technometrics · doi:10.1198/004017005000000517 · Cited by 342 · cited 2×
“Gelman and Pardoe [15] introduced an extension of themultilevelR2 proposed by Snijders and Bosker so that an arbitrary number of levels could bemodeled, but the technical detail involved in applying themethod acts as a deterrent for investigators that do not have the necessary statistical background.”
BackgroundMethod
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“Finally, we used the Glimmix_R2 macro (Jaeger et al., 2017) in SAS to estimate R 2 effect sizes for each model.”
MethodTeachers’ preference for later school start times
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Metadata
- Authors
- Jaeger, B. C., Edwards, L. J., Das, K., & Sen, P. K.
- Venue
- Journal of Applied Statistics
- Publisher
- Informa UK Limited
- Published
- 2016-06-08
- Volume
- 44
- Issue
- 6
- Pages
- 1086-1105
- ISSN
- 0266-4763 (ISSN-L)
- 1360-0532
- OpenAlex
- W2410090949
- Cited by
- 399
- References
- 2
- FWCI
- 28.57
- Type
- journal article
- Language
- en
- Open access
- closed
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