Maximum Likelihood for Generalized Linear Models with Nested Random Effects via High-Order, Multivariate Laplace Approximation

By Stephen Raudenbush, Mengxue Yang, M. Yosef. 2000

434 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/a3425102781931ac3c379062ab1d259837603684

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Citations in the corpus

6. A Multivariate, Multilevel Rasch Model with Application to Self-Reported Criminal Behavior (2003, methodology): “This can be accomplished using penalized quasilikelihood (see Raudenbush et al. 2000).4 We found that the conditional variance of the item responses was significantly lower than expected under a Bernoulli model.”
A Two-Part Random-Effects Model for Semicontinuous Longitudinal Data (2001, methodology): “Raudenbush et al. (2000) approximated the log-likelihood for GLMMs by a sixth-order Laplace expansion.”
A Stochastic Variational Framework for Fitting and Diagnosing Generalized Linear Mixed Models (2012, methodology): “Other approximate methods include penalized quasi-likelihood (Breslow et al. , 1993) and Laplace approximation and its extensions (Raudenbush et al. , 2000).”
Simplex Mixed‐Effects Models for Longitudinal Proportional Data (2008, methodology): “This bias correction approach has been applied by Shun & McCullagh (1995), Shun (1997) and Raudenbush et al. (2000) for the case of binary data, where an approximation based on the sixth-order Taylor expansion was considered.”
Marriage and Desistance from Crime in the Netherlands: Do Gender and Socio-Historical Context Matter? (2009, methodology): “We estimate a multilevel model using Generalized Hierarchical Linear Modeling (HLM) version 6.04 (Raudenbush et al. 2007).”
Bayesian and likelihood-based methods in multilevel modeling 1 A comparison of Bayesian and likelihood-based methods for fitting multilevel models (2006, methodology): “…Section 5 for a software discussion); (b) the nonparametric maximum likelihood methods of Aitkin (1999a); (c) the Laplace-approximation approach of Raudenbush et al. (2000); (d) the work on hierarchical generalized linear models of Lee and Nelder (2000); and (e) interval estimation based on…”
Nonlinear models for repeated measurement data: An overview and update (2003, neutral): “Raudenbush et al. (2000) discuss use of a sixth-order”
Handbook of multilevel analysis (2008, methodology): “Proofs of the first three results are given, for example, in de Leeuw and Liu [31].”
Mixtures of g-Priors in Generalized Linear Models (2015, methodology): “Under canonical links, a correction factor derived based on a sixth-order Laplace approximation (Raudenbush et al. 2000) can be readily applied to mixtures of g-priors and local EB estimates, as the correction factor does not depend on g (Sabanés Bové and Held 2011).”
p2: a random effects model with covariates for directed graphs (2004, background): “…(1994) and GOLDSTEIN and RASBASH (1996); numerical integration by HEDEKER and GIBBONS (1997), see also RABEHESKETH, PICKLES and SKONDRAL (2001); stochastic EM by MCCULLOCH (1997); nonparametric (latent class) EM by AITKIN (1999); and Laplace approximation by RAUDENBUSH, YANG, and YOSEF (2000).”
Random effect models for repeated measures of zero-inflated count data (2005, methodology): “To maximize this approximation for the likelihood function, we use an approximate version of the Fisher scoring method (Green, 1984; Raudenbush et al., 2000) to obtain ŵ.”