Counting degrees of freedom in hierarchical and other richly-parameterised models

By James S. Hodges, D. Sargent. 2001

179 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Environmental Engineering, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/7327c38aa637166820eeb44c5124f430aeace23a

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Citations in the corpus

A unifying approach to the estimation of the conditional Akaike information in generalized linear mixed models (2014, background): “…random effects variance parameters ϑ they show that an asymptotically unbiased estimator of the conditional Akaike information is cAIC = −2 log f(y|β̂, û) + 2(ρ+ 1), where ρ = tr [( XtX XtZ ZtX ZtZ + σ2G(ϑ)−1 )−1 ( XtX XtZ ZtX ZtZ )] are the effective degrees of freedom (Hodges & Sargent (2001)).”
Generalized additive models for location, scale and shape (2005, background): “This has been considered by Hodges and Sargent (2001).”
Deviance information criteria for missing data models (2006, methodology): “(Although this is not in direct connection with our missing data set-up, nor with the DIC criterion, note that Hodges and Sargent (2001) also describes the derivation of degrees of freedom in loosely parameterised models.)”
Estimating the Integrated Likelihood via Posterior Simulation Using the Harmonic Mean Identity (2006, background): “Other recent work in this area includes that of Lu et al. (2004), who extended the approach of Hodges and Sargent (2001) to generalized linear mixed model settings, obtaining effective model size estimates that respect both the lower (0) and upper (raw parameter count) boundaries.”
Model Selection in Linear Mixed Models (2013, methodology): “is the effective degrees of freedom used in estimating β and v (Hodges and Sargent (2001)). The effective degrees of freedom satisfies p≤ ρ(τ )≤ p+ s so lies between the degrees of freedom of the regression model without v and the regression model treating v as fixed effects (Vaida and Blanchard (20”
Empirical Bayes: Past, Present and Future (2000, background): “But recent work by Hodges and Sargent (2001) and Natarajan and Kass (2000) showed that such hyperpriors, though appearing “noninformative,” can actually have significant impact on the resulting posterior distributions.”
A unified approach to model selection using the likelihood ratio test (2011, background): “In richly parameterisedmodels, such as those containing random effects, estimating the number of degrees of freedom (or alternatively the number of ‘effective’ parameters) is neither straightforward nor necessarily unambiguous (Hodges & Sargent 2001).”
Fence methods for mixed model selection (2008, unknown): “By Taylor expansion, (18) and iii), we havê QM = QM + (∂QM/∂θM )(θ̂M − θM ) + (1/2)(θ̂M − θM ){∂(2)QM/∂θM∂θ M |θ̃M }(θ̂M−θM ) = QM +R2, whereθ̃M lies betweenθM andθ̂M .”
Asymptotic Equivalence between Cross-Validations and Akaike Information Criteria in Mixed-Effects Models (2021, methodology): “Lemma 1 was proved in Hodges and Sargent (2001) and was used in Vaida and Blanchard (2005) and Liang et al. (2008).”
Spatial modelling using a new class of nonstationary covariance functions (2006, background): “This induces a prior on the covariance structure (Hodges and Sargent 2001).”
Bayesian Measures of Explained Variance and Pooling in Multilevel (Hierarchical) Models (2006, methodology): “Our proposed pooling factor is also related to the notion of “effective number of parameters”—see Hodges and Sargent (2001), Vaida (2004), and Hastie and Tibshirani (1990).”
Model Selection in the Presence of Incidental Parameters (2015, unknown): “The additional penalty depends on a proper model complexity measure (e.g., Rissanen, 1986; Bozdogan, 2000; Hodges and Sargent, 2001) that reflects the level of difficulty of estimation.”
Bayesian measures of model complexity and fit (2002, methodology): “If all group precisions are equal, pD = 1 + .p− 1/ρ; as obtained by Hodges and Sargent (2001).”