Efficient Laplacian and Adaptive Gaussian Quadrature Algorithms for Multilevel Generalized Linear Mixed Models

By J. Pinheiro, Edward C. Chao. 2006

298 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2952ef46f2a8dfcc3a08505933d1f9e74af01919

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Citations in the corpus

Multilevel Modelling of Country Effects: A Cautionary Tale (2016, methodology): “…been found to produce more accurate estimates than penalized quasi-likelihood both with data structures different from ours (Rodriguez and Goldman, 2001; Callens and Croux, 2005; Pinheiro and Chao, 2006; Austin, 2010) and also with the same data structure as used in this article (Jenkins, 2013).”
Small Sample Size Solutions (2020, background): “With large samples, simulations have shown that numerical approximation is superior to Taylor expansion (Pinheiro & Chao, 2006).”
On the Unnecessary Ubiquity of Hierarchical Linear Modeling (2017, methodology): “Table 7 compares estimates from an HLM estimated with PQL, HLM estimated with AGQ and 10 integration points (as recommended by Pinheiro & Bates, 1995; Pinheiro & Chao, 2006), and GEE with an independent working correlation matrix.”
Regression Analysis of Country Effects Using Multilevel Data: A Cautionary Tale (2013, methodology): “Simulations by Browne and Draper (2000) and Pinheiro and Chao (2006) re-used the three-level data structure employed by Rodriguez and Goldman (1995) with relatively small NC.”
Linear quantile mixed models (2013, background): “The marginal density in (4) can be characterized by using Theorem 6 by Prékopa (1973).”
Testing environmental and genetic effects in the presence of spatial autocorrelation (2014, methodology): “2008), is usually a less accurate approximation of the likelihood, up to the point where it has been considered ‘not truly an approximation to the likelihood function’ and not allowing the use of likelihood ratio tests (Pinheiro and Chao 2006).”
Mixed and Mixture Regression Models for Continuous Bounded Responses Using the Beta Distribution (2012, methodology): “These topics raise some open questions in the GLMM literature generally.”
Random effects meta‐analysis of event outcome in the framework of the generalized linear mixed model with applications in sparse data (2010, background): “However, both methods have been reported to produce biased estimates in certain cases of practical interest, most noticeable that of binary outcome with few observations per group [17, 18].”