Optimization in Generalized Linear Models: a Case Study
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Outros Autores: | , |
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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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 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.22/10195 |
url |
http://hdl.handle.net/10400.22/10195 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1063/1.4952094 |
dc.rights.driver.fl_str_mv |
metadata only access info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
metadata only access |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
American Institute of Physics |
publisher.none.fl_str_mv |
American Institute of Physics |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799131402532290560 |