Bayesian Measures of Explained Variance and Pooling in Multilevel (Hierarchical) Models

By Andrew Gelman, Iain Pardoe. Technometrics, 2006

345 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/3b8e7ac8b4ef22cb0a50381be13ac9edc91c7341

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Citations in the corpus

A general and simple method for obtaining R2 from generalized linear mixed‐effects models (2013, background): “The second problem of extendingR21 andR 2 2 to models with more than two levels was addressed by Gelman & Pardoe (2006), who provide a solution to extend R21 and R 2 2 to any arbitrary numbers of levels (or random factors) in a Bayesian framework.”
Conspecific and phylogenetic density‐dependent survival differs across life stages in a tropical forest (2015, methodology): “To examine neighbourhood effects on individual survival at multiple life-history stages, we used generalized linear mixed-effects models (GLMMs; Gelman & Pardoe 2006; Bolker et al. 2009) with binomial errors to model individual survival (lived/died) as a function of conspecific neighbour density,…”
Advanced conjoint analysis using feature selection via support vector machines (2015, neutral): “[36, 44] 3 [6, 16, 39] 3 [3, 5, 13, 17, 19, 20, 26, 29, 31, 35, 43] 3 [7, 22, 32, 33] 3 3 [10, 11, 14, 15, 42] 3 3 [2] 3 3 This study 3 3 3”
A brief introduction to mixed effects modelling and multi-model inference in ecology (2018, methodology): “Gelman & Pardoe (2006) derived a measure of R 2 that accounts for the hierarchical nature of LMMs and gives a measure for both group and unit level regressions (see also Gelman & Hill 2007 p. 474), but it was developed for a Bayesian framework and a frequentist analogue does not appear to be widely…”
Emotion-Induced Engagement in Internet Video Advertisements (2012, background): “The GPR2 for the first level of the full model is 63% and confirms that the sets of variables jointly explain a significant portion of the variance in observed zapping.”
Measurement Invariance Testing with Many Groups: A Comparison of Five Approaches (2017, methodology): “Beyond expressing uncertainty, researchers are allowed to incorporate prior knowledge on parameters (e.g., factor loadings) in data analysis (Gelman & Pardoe, 2006; Muthén & Asparouhov, 2012) by specifying a prior distribution of a parameter in the model.”
Quantifying explained variance in multilevel models: An integrative framework for defining R-squared measures. (2019, methodology): “…our framework to these other existing individual measures that are, for instance, computed under a Bayesian framework using posterior simulation (Gelman & Pardoe, 2006), derived from likelihood ratio tests or Wald tests (Edwards et al., 2008; Jaeger et al., 2017; Magee, 1990), represented as…”
Understanding the Impact of Microcredit Expansions: A Bayesian Hierarchical Analysis of 7 Randomised Experiments (2015, neutral): “Bayesian hierarchical models come equipped with several natural metrics to assess the extent of pooling across sites shown in the posterior distribution, developed and studied by statisticians (Gelman et al 2004, Gelman and Pardoe 2006).”
Efficient Ranking in Sponsored Search (2011, methodology): “For each draw γ was estimated using the following approach proposed by Gelman and Pardoe [7].”
R 2 STATISTICS FOR MIXED MODELS (2005, methodology): “A Bayesian R(2) for these same kinds of models is described by Gelman and Pardoe (2004). This paper differs from others in extending the concept of R(2) to mixed models with random (block) effects and spatially correlated residuals, the kinds of models commonly used by researchers in designed experi”
An R2 statistic for fixed effects in the generalized linear mixed model (2017, methodology): “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”