Optimization in Generalized Linear Models: a Case Study

Detalhes bibliográficos
Autor(a) principal: Silva, Eliana Costa e
Data de Publicação: 2016
Outros Autores: Correia, Aldina, Lopes, Isabel Cristina
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.22/10195
Resumo: The maximum likelihood method is usually chosen to estimate the regression parameters of Generalized Linear Models (GLM) and also for hypothesis testing and goodness of fit tests. The classical method for estimating GLM parameters is the Fisher scores. In this work we propose to compute the estimates of the parameters with two alternative methods: a derivative-based optimization method, namely the BFGS method which is one of the most popular of the quasi-Newton algorithms, and the PSwarm derivative-free optimization method that combines features of a pattern search optimization method with a global Particle Swarm scheme. As a case study we use a dataset of biological parameters (phytoplankton) and chemical and environmental parameters of the water column of a Portuguese reservoir. The results show that, for this dataset, BFGS and PSwarm methods provided a better fit, than Fisher scores method, and can be good alternatives for finding the estimates for the parameters of a GLM.
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spelling Optimization in Generalized Linear Models: a Case StudyNonlinear OptimizationGeneralized Linear ModelsGamma DistributionInferenceWater QualityThe maximum likelihood method is usually chosen to estimate the regression parameters of Generalized Linear Models (GLM) and also for hypothesis testing and goodness of fit tests. The classical method for estimating GLM parameters is the Fisher scores. In this work we propose to compute the estimates of the parameters with two alternative methods: a derivative-based optimization method, namely the BFGS method which is one of the most popular of the quasi-Newton algorithms, and the PSwarm derivative-free optimization method that combines features of a pattern search optimization method with a global Particle Swarm scheme. As a case study we use a dataset of biological parameters (phytoplankton) and chemical and environmental parameters of the water column of a Portuguese reservoir. The results show that, for this dataset, BFGS and PSwarm methods provided a better fit, than Fisher scores method, and can be good alternatives for finding the estimates for the parameters of a GLM.American Institute of PhysicsRepositório Científico do Instituto Politécnico do PortoSilva, Eliana Costa eCorreia, AldinaLopes, Isabel Cristina2017-08-07T10:15:33Z20162016-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.22/10195eng10.1063/1.4952094metadata only accessinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-03-13T12:51:44Zoai:recipp.ipp.pt:10400.22/10195Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:30:40.471257Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Optimization in Generalized Linear Models: a Case Study
title Optimization in Generalized Linear Models: a Case Study
spellingShingle Optimization in Generalized Linear Models: a Case Study
Silva, Eliana Costa e
Nonlinear Optimization
Generalized Linear Models
Gamma Distribution
Inference
Water Quality
title_short Optimization in Generalized Linear Models: a Case Study
title_full Optimization in Generalized Linear Models: a Case Study
title_fullStr Optimization in Generalized Linear Models: a Case Study
title_full_unstemmed Optimization in Generalized Linear Models: a Case Study
title_sort Optimization in Generalized Linear Models: a Case Study
author Silva, Eliana Costa e
author_facet Silva, Eliana Costa e
Correia, Aldina
Lopes, Isabel Cristina
author_role author
author2 Correia, Aldina
Lopes, Isabel Cristina
author2_role author
author
dc.contributor.none.fl_str_mv Repositório Científico do Instituto Politécnico do Porto
dc.contributor.author.fl_str_mv Silva, Eliana Costa e
Correia, Aldina
Lopes, Isabel Cristina
dc.subject.por.fl_str_mv Nonlinear Optimization
Generalized Linear Models
Gamma Distribution
Inference
Water Quality
topic Nonlinear Optimization
Generalized Linear Models
Gamma Distribution
Inference
Water Quality
description The maximum likelihood method is usually chosen to estimate the regression parameters of Generalized Linear Models (GLM) and also for hypothesis testing and goodness of fit tests. The classical method for estimating GLM parameters is the Fisher scores. In this work we propose to compute the estimates of the parameters with two alternative methods: a derivative-based optimization method, namely the BFGS method which is one of the most popular of the quasi-Newton algorithms, and the PSwarm derivative-free optimization method that combines features of a pattern search optimization method with a global Particle Swarm scheme. As a case study we use a dataset of biological parameters (phytoplankton) and chemical and environmental parameters of the water column of a Portuguese reservoir. The results show that, for this dataset, BFGS and PSwarm methods provided a better fit, than Fisher scores method, and can be good alternatives for finding the estimates for the parameters of a GLM.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-01-01T00:00:00Z
2017-08-07T10:15:33Z
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publisher.none.fl_str_mv American Institute of Physics
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