Gauss-Seidel estimation of generalized linear mixed models with application to poisson modeling of spatially varying disease rates

Guha, S; Ryan, L; Morara, M

Gauss-Seidel estimation of generalized linear mixed models with application to poisson modeling of spatially varying disease rates

Guha, S Ryan, L

Morara, M

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Publication Type:: Journal Article
Citation:: Journal of Computational and Graphical Statistics, 2009, 18 (4), pp. 818 - 837
Issue Date:: 2009-12-28

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Field	Value	Language
dc.contributor.author	Guha, S	en_US
dc.contributor.author	Ryan, L https://orcid.org/0000-0001-5957-2490	en_US
dc.contributor.author	Morara, M	en_US
dc.date.issued	2009-12-28	en_US
dc.identifier.citation	Journal of Computational and Graphical Statistics, 2009, 18 (4), pp. 818 - 837	en_US
dc.identifier.issn	1061-8600	en_US
dc.identifier.uri	http://hdl.handle.net/10453/31559
dc.description.abstract	Generalized linear mixed models (GLMMs) are often fit by computational procedures such as penalized quasi-likelihood (PQL). Special cases of GLMMs are generalized linear models (GLMs), which are often fit using algorithms like iterative weighted least squares (IWLS). High computational costs and memory space constraints make it difficult to apply these iterative procedures to datasets having a very large number of records. We propose a computationally efficient strategy based on the Gauss-Seidel algorithm that iteratively fits submodels of the GLMM to collapsed versions of the data. The strategy is applied to investigate the relationship between ischemic heart disease, socioeconomic status, and age/gender category in New South Wales, Australia, based on outcome data consisting of approximately 33 million records. For Poisson and binomial regression models, the Gauss-Seidel approach is found to substantially outperform existing methods in terms of maximum analyzable sample size. Remarkably, for both models, the average time per iteration and the total time until convergence of the Gauss-Seidel procedure are less than 0.3% of the corresponding times for the IWLS algorithm. Platform-independent pseudo-code for fitting GLMS, as well as the source code used to generate and analyze the datasets in the simulation studies, are available online as supplemental materials. © 2009 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.	en_US
dc.relation.ispartof	Journal of Computational and Graphical Statistics	en_US
dc.relation.isbasedon	10.1198/jcgs.2009.06127	en_US
dc.subject.classification	Statistics & Probability	en_US
dc.title	Gauss-Seidel estimation of generalized linear mixed models with application to poisson modeling of spatially varying disease rates	en_US
dc.type	Journal Article
utslib.citation.volume	4	en_US
utslib.citation.volume	18	en_US
utslib.for	0104 Statistics	en_US
utslib.for	1403 Econometrics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	closed_access
pubs.issue	4	en_US
pubs.publication-status	Published	en_US
pubs.volume	18	en_US

Abstract:

Generalized linear mixed models (GLMMs) are often fit by computational procedures such as penalized quasi-likelihood (PQL). Special cases of GLMMs are generalized linear models (GLMs), which are often fit using algorithms like iterative weighted least squares (IWLS). High computational costs and memory space constraints make it difficult to apply these iterative procedures to datasets having a very large number of records. We propose a computationally efficient strategy based on the Gauss-Seidel algorithm that iteratively fits submodels of the GLMM to collapsed versions of the data. The strategy is applied to investigate the relationship between ischemic heart disease, socioeconomic status, and age/gender category in New South Wales, Australia, based on outcome data consisting of approximately 33 million records. For Poisson and binomial regression models, the Gauss-Seidel approach is found to substantially outperform existing methods in terms of maximum analyzable sample size. Remarkably, for both models, the average time per iteration and the total time until convergence of the Gauss-Seidel procedure are less than 0.3% of the corresponding times for the IWLS algorithm. Platform-independent pseudo-code for fitting GLMS, as well as the source code used to generate and analyze the datasets in the simulation studies, are available online as supplemental materials. © 2009 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

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http://hdl.handle.net/10453/31559