Convergence theorems in multinomial saturated and logistic models
In this paper, we develop a theoretical study about the logistic and saturated multinomial models when the response variable takes one of R ≥ 2 levels. Several theorems on the existence and calculations of the maximum likelihood (ML) estimates of the parameters of both models are presented and demon...
- Autores:
-
Orozco-Acosta, Erick
Llinás-Solano, Humberto
Fonseca-Rodríguez, Javier
- Tipo de recurso:
- Fecha de publicación:
- 2020
- Institución:
- Universidad Simón Bolívar
- Repositorio:
- Repositorio Digital USB
- Idioma:
- eng
- OAI Identifier:
- oai:bonga.unisimon.edu.co:20.500.12442/6233
- Acceso en línea:
- https://hdl.handle.net/20.500.12442/6233
http://dx.doi.org/10.15446/rce.v43n2.79151
https://revistas.unal.edu.co/index.php/estad/article/view/79151
- Palabra clave:
- Multinomial logit model
Saturated model
Logistic regression
Maximum likelihood estimator
Score vector
Fisher information matrix
Modelo logístico multinomial
Modelo saturado
Regresión logística
Estimador de máxima verosimilitud
Vector score
Matriz de información de Fisher
- Rights
- openAccess
- License
- Attribution-NonCommercial-NoDerivatives 4.0 Internacional
| id |
USIMONBOL2_7fb224e3e1f66bd443f37c78acc787b1 |
|---|---|
| oai_identifier_str |
oai:bonga.unisimon.edu.co:20.500.12442/6233 |
| network_acronym_str |
USIMONBOL2 |
| network_name_str |
Repositorio Digital USB |
| repository_id_str |
|
| dc.title.eng.fl_str_mv |
Convergence theorems in multinomial saturated and logistic models |
| dc.title.translated.spa.fl_str_mv |
Teoremas de convergencias en los modelos saturados y logísticos multinomiales |
| title |
Convergence theorems in multinomial saturated and logistic models |
| spellingShingle |
Convergence theorems in multinomial saturated and logistic models Multinomial logit model Saturated model Logistic regression Maximum likelihood estimator Score vector Fisher information matrix Modelo logístico multinomial Modelo saturado Regresión logística Estimador de máxima verosimilitud Vector score Matriz de información de Fisher |
| title_short |
Convergence theorems in multinomial saturated and logistic models |
| title_full |
Convergence theorems in multinomial saturated and logistic models |
| title_fullStr |
Convergence theorems in multinomial saturated and logistic models |
| title_full_unstemmed |
Convergence theorems in multinomial saturated and logistic models |
| title_sort |
Convergence theorems in multinomial saturated and logistic models |
| dc.creator.fl_str_mv |
Orozco-Acosta, Erick Llinás-Solano, Humberto Fonseca-Rodríguez, Javier |
| dc.contributor.author.none.fl_str_mv |
Orozco-Acosta, Erick Llinás-Solano, Humberto Fonseca-Rodríguez, Javier |
| dc.subject.eng.fl_str_mv |
Multinomial logit model Saturated model Logistic regression Maximum likelihood estimator Score vector Fisher information matrix Modelo logístico multinomial |
| topic |
Multinomial logit model Saturated model Logistic regression Maximum likelihood estimator Score vector Fisher information matrix Modelo logístico multinomial Modelo saturado Regresión logística Estimador de máxima verosimilitud Vector score Matriz de información de Fisher |
| dc.subject.spa.fl_str_mv |
Modelo saturado Regresión logística Estimador de máxima verosimilitud Vector score Matriz de información de Fisher |
| description |
In this paper, we develop a theoretical study about the logistic and saturated multinomial models when the response variable takes one of R ≥ 2 levels. Several theorems on the existence and calculations of the maximum likelihood (ML) estimates of the parameters of both models are presented and demonstrated. Furthermore, properties are identified and, based on an asymptotic theory, convergence theorems are tested for score vectors and information matrices of both models. Finally, an application of this theory is presented and assessed using data from the R statistical program. |
| publishDate |
2020 |
| dc.date.accessioned.none.fl_str_mv |
2020-07-22T17:18:09Z |
| dc.date.available.none.fl_str_mv |
2020-07-22T17:18:09Z |
| dc.date.issued.none.fl_str_mv |
2020 |
| dc.type.coarversion.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
| dc.type.coar.fl_str_mv |
http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.type.driver.eng.fl_str_mv |
info:eu-repo/semantics/article |
| dc.type.spa.spa.fl_str_mv |
Artículo científico |
| dc.identifier.issn.none.fl_str_mv |
01201751 |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/20.500.12442/6233 |
| dc.identifier.doi.none.fl_str_mv |
http://dx.doi.org/10.15446/rce.v43n2.79151 |
| dc.identifier.url.none.fl_str_mv |
https://revistas.unal.edu.co/index.php/estad/article/view/79151 |
| identifier_str_mv |
01201751 |
| url |
https://hdl.handle.net/20.500.12442/6233 http://dx.doi.org/10.15446/rce.v43n2.79151 https://revistas.unal.edu.co/index.php/estad/article/view/79151 |
| dc.language.iso.eng.fl_str_mv |
eng |
| language |
eng |
| dc.rights.none.fl_str_mv |
Attribution-NonCommercial-NoDerivatives 4.0 Internacional |
| dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
| dc.rights.uri.none.fl_str_mv |
http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| dc.rights.accessrights.eng.fl_str_mv |
info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ http://purl.org/coar/access_right/c_abf2 |
| eu_rights_str_mv |
openAccess |
| dc.format.mimetype.spa.fl_str_mv |
pdf |
| dc.publisher.spa.fl_str_mv |
Universidad Nacional de Colombia |
| dc.source.spa.fl_str_mv |
Revista Colombiana de Estadística - Theoretical Statistics |
| dc.source.none.fl_str_mv |
Vol. 43, N° 2, (2020) |
| institution |
Universidad Simón Bolívar |
| bitstream.url.fl_str_mv |
https://bonga.unisimon.edu.co/bitstreams/6962a744-ec25-4442-b50c-5a352880a1fd/download https://bonga.unisimon.edu.co/bitstreams/dce38083-d941-4eac-8b44-e88634293145/download https://bonga.unisimon.edu.co/bitstreams/7f790951-6978-4f39-901d-2d21e941c2b2/download https://bonga.unisimon.edu.co/bitstreams/a51668bf-94e5-49dc-b00e-535ae8470d54/download https://bonga.unisimon.edu.co/bitstreams/d598c6be-d125-4d31-8d44-1a8e96dbab90/download https://bonga.unisimon.edu.co/bitstreams/4274b48d-5771-4899-9403-4823eebf0242/download https://bonga.unisimon.edu.co/bitstreams/5b7b0f70-367a-4d8a-bde2-8543eb7937d9/download |
| bitstream.checksum.fl_str_mv |
894e63ecd4bfc71abfa9bf5fb17d8fe5 4460e5956bc1d1639be9ae6146a50347 733bec43a0bf5ade4d97db708e29b185 f14d1b41317f21b1ff64f5f505198796 db35c60415ba6b4d102945a5b73c8000 f292dbc9fd72e87ea76664875ec8fb06 1038a1e7ca88333738c96c4c100c34b8 |
| bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 MD5 MD5 MD5 |
| repository.name.fl_str_mv |
Repositorio Digital Universidad Simón Bolívar |
| repository.mail.fl_str_mv |
repositorio.digital@unisimon.edu.co |
| _version_ |
1814076114009587712 |
| spelling |
Orozco-Acosta, Erick5d37d2d9-817f-47a8-b536-38d6cdaaac3dLlinás-Solano, Humberto9be5f07c-1116-4ce7-9c3d-53d0c4287640Fonseca-Rodríguez, Javiere538b229-5819-4fbe-b2dc-7757ca1f7e2a2020-07-22T17:18:09Z2020-07-22T17:18:09Z202001201751https://hdl.handle.net/20.500.12442/6233http://dx.doi.org/10.15446/rce.v43n2.79151https://revistas.unal.edu.co/index.php/estad/article/view/79151In this paper, we develop a theoretical study about the logistic and saturated multinomial models when the response variable takes one of R ≥ 2 levels. Several theorems on the existence and calculations of the maximum likelihood (ML) estimates of the parameters of both models are presented and demonstrated. Furthermore, properties are identified and, based on an asymptotic theory, convergence theorems are tested for score vectors and information matrices of both models. Finally, an application of this theory is presented and assessed using data from the R statistical program.En este artículo se desarrolla un estudio teórico de los modelos logísticos y saturados multinomiales cuando la variable de respuesta toma uno de R ≥ 2 niveles. Se presentan y demuestran teoremas sobre la existencia y cálculos de las estimaciones de máxima verosimilitud (ML-estimaciones) de los parámetros de ambos modelos. Se encuentran sus propiedades y, usando teoría asintótica, se prueban teoremas de convergencia para los vectores de puntajes y para las matrices de información. Se presenta y analiza una aplicación de esta teoría con datos tomados de la librería aplore3 del programa R.pdfengUniversidad Nacional de ColombiaAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Revista Colombiana de Estadística - Theoretical StatisticsVol. 43, N° 2, (2020)Multinomial logit modelSaturated modelLogistic regressionMaximum likelihood estimatorScore vectorFisher information matrixModelo logístico multinomialModelo saturadoRegresión logísticaEstimador de máxima verosimilitudVector scoreMatriz de información de FisherConvergence theorems in multinomial saturated and logistic modelsTeoremas de convergencias en los modelos saturados y logísticos multinomialesinfo:eu-repo/semantics/articleArtículo científicohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1Agresti, A. (2013), Categorical Data Analysis, Wiley Series in Probability and Statistics, 3 edn, John Wiley and Sons.Anderson, C., Verkuilen, J. & Peyton, B. (2010), ‘Modeling polytomous item responses using simultaneously estimated multinomial logistic regression models’, Journal of Educational and Behavioral Statistics 35(4), 422–452.Begg, C. B. & Gray, R. (1984), ‘Calculation of polychotomous logistic regression parameters using individualized regressions’, Biometrika 71(1), 11–18.Chan, Y. H. (2005), ‘Biostatistics 305. multinomial logistic regression’, Singapore medical journal 46(6), 259–269.Chen, Y.-H. & Kao, J.-T. (2006), ‘Multinomial logistic regression approach to haplotype association analysis in population-based case-control studies’, BMC Genetics 7(1), 1–12.Chuang, H.-L. (1997), ‘High school youths’ dropout and re-enrollment behavior’, Economics of Education Review 16(2), 171–186.Cox, D. R. (1958), ‘The regression analysis of binary sequences’, Journal of the Royal Statistical Society: Series B (Methodological) 20(2), 215–232.Darlington, R. B. (1990), Regression and linear models, McGraw-Hill College.Dessens, J., Jansen, W., G. B. Jansen, W., Ganzeboom, B. & Van der Heijden, P. (2003), ‘Patterns and trends in occupational attainment of first jobs in the netherlands, 1930-1995: Ordinary least squares regression versus conditional multinomial logistic regression’, Journal of the Royal Statistical Society. Series A (Statistics in Society) 166(1), 63–84.Ekström, M., Esseen, P.-A., Westerlund, B., Grafström, A., Jonsson, B. & Ståhl, G. (2018), ‘Logistic regression for clustered data from environmental monitoring programs’, Ecological Informatics 43, 165 – 173.Exavery, A., Mbaruku, G., Mbuyita, S., Makemba, A., Kinyonge, I. & Kweka, H. (2014), ‘Factors affecting uptake of optimal doses of sulphadoxinepyrimethamine for intermittent preventive treatment of malaria in pregnancy in six districts of tanzania’, Malaria Journal 13(1), 2–9.Fahrmeir, L. & Kaufmann, H. (1985), ‘Consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models’, Annals of Statistic 13(1), 342–368.Fontanella, C. A., Early, T. J. & Phillips, G. (2008), ‘Need or availability? modeling aftercare decisions for psychiatrically hospitalized adolescents’, Children and Youth Services Review 30(7), 758 – 773.Harrell, F. (2015), Regression Modeling Strategies: With Applications to Linear Models, Logistic and Ordinal Regression, and Survival Analysis, Springer Series in Statistics, Springer International Publishing.Harville, D. (1997), Matrix algebra from a statistician’s perspective, Springer- Verlag.Hosmer, D. & Lemeshow, S. (2000), Applied logistic regression, Wiley Series in Probability and Statistics, second edition edn, John Wiley & Sons Inc.Kim, J. (2015), ‘School socioeconomic composition and adolescent sexual initiation in malawi’, Studies in Family Planning 46(3), 263–279.Kleinbaum, D. & Klein, M. (2010), Logistic Regression. A Self-Learning Text, Statistics for Biology and Health, third edition edn, Springer-Verlag New York.LLinás, H. (2006), ‘Precisiones en la teoría de los modelos logísticos’, Revista Colombiana de Estadística 29(2), 239–265.LLinás, H. & Carreño, C. (2012), ‘The multinomial logistic model for the case inwhich the response variable can assume one ofthree levels and related models’, Revista Colombiana de Estadística 35(1), 131–138.Lloyd, C. J. & Frommer, D. J. (2008), ‘An application of multinomial logistic regression to estimating performance of a multiple-screening test with incomplete verification’, Journal of the Royal Statistical Society. Series C (Applied Statistics) 57(1), 89–102.Long, J. S. (1987), ‘A graphical method for the interpretation of multinomial logit analysis’, Sociological Methods & Research 15(4), 420–446.McCullagh, P. (1983), ‘Quasi-likelihood functions’, The Annals of Statistics 11(1), 59–67.McCullagh, P. & Neider, J. (2018), Generalized Linear Models, CRC Press.McFadden, D. (1973), Conditional Logit Analysis of Qualitative Choice Behavior, BART impact studies final report series: Traveler behavior studies, Institute of Urban and Regional Development, University of California.McNevin, D., Santos, C., Gamez-Tato, A., Álvarez-Dios, J., Casares, M., Daniel, R., Phillips, C. & Lareu, M. (2013), ‘An assessment of bayesian and multinomial logistic regression classification systems to analyse admixed individuals’, Forensic Science International: Genetics Supplement Series 4(1), 63 – 64.Monyai, S., Lesaoana, M., Darikwa, T. & Nyamugure, P. (2016), ‘Application of multinomial logistic regression to educational factors of the 2009 general household survey in south africa’, Journal of Applied Statistics 43(1), 128–139.Peng, C.-Y. J., Lee, K. L. & Ingersoll, G. M. (2002), ‘An introduction to logistic regression analysis and reporting’, The journal of educational research 96(1), 3–14.Pohlman, J. & Leitner, D. (2003), ‘A comparison of ordinary least squares and logistic regression’, The Ohio journal of science 103, 118–125.Rao, C. R., Rao, C. R., Statistiker, M., Rao, C. R. & Rao, C. R. (1973), Linear statistical inference and its applications, Vol. 2, Wiley New York.Schnor, C., Vanassche, S. & Bavel, J. (2017), ‘Stepfather or biological father? education-specific pathways of postdivorce fatherhood’, Demographic Research 37, 1659–1694.Tan, Q., Christiansen, L., Christensen, K., Kruse, T. A. & Bathum, L. (2004), ‘Apolipoprotein e genotype frequency patterns in aged danes as revealed by logistic regression models’, European Journal of Epidemiology 19(7), 651–656. *http://www.jstor.org/stable/3582754Tilano, J. & Arteta, M. (2012), Modelos logísticos multinomiales: estimaciones, pruebas y selección de modelos, Master’s thesis, Universidad del Norte.Wedderburn, R. W. M. (1974), ‘Quasi-likelihood functions, generalized linear models, and the gauss-newton method’, Biometrika 61(3), 439–447.Wedderburn, R. W. M. (1976), ‘On the existence and uniqueness of the maximum likelihood estimates for certain generalized linear models’, Biometrika 63(1), 27–32.Zacks, S. (1971), The Theory of Statistical Inference, Wiley series in probability and mathematical statistics, John Wiley.Díaz, L. & Morales, M. (2009), Análisis estadístico de datos categóricos, Editorial Universidad Nacional de Colombia.LLinás, H., Arteta, M. & Tilano, J. (2016), ‘El modelo de regresión logística para el caso en que la variable de respuesta puede asumir uno de tres niveles: estimaciones, pruebas de hipótesis y selección de modelos’, Revista de Matemática: Teoría y Aplicaciones 23(1), 173–197.Monroy, L., Morales, M. & Dávila, L. (2018), Análisis estadístico de datos categóricos, Universidad Nacional de Colombia.ORIGINALPDF.pdfPDF.pdfPDFapplication/pdf183748https://bonga.unisimon.edu.co/bitstreams/6962a744-ec25-4442-b50c-5a352880a1fd/download894e63ecd4bfc71abfa9bf5fb17d8fe5MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://bonga.unisimon.edu.co/bitstreams/dce38083-d941-4eac-8b44-e88634293145/download4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-8381https://bonga.unisimon.edu.co/bitstreams/7f790951-6978-4f39-901d-2d21e941c2b2/download733bec43a0bf5ade4d97db708e29b185MD53TEXTConvergtheoremultinomisaturandlogimodels.pdf.txtConvergtheoremultinomisaturandlogimodels.pdf.txtExtracted texttext/plain47960https://bonga.unisimon.edu.co/bitstreams/a51668bf-94e5-49dc-b00e-535ae8470d54/downloadf14d1b41317f21b1ff64f5f505198796MD54PDF.pdf.txtPDF.pdf.txtExtracted texttext/plain48761https://bonga.unisimon.edu.co/bitstreams/d598c6be-d125-4d31-8d44-1a8e96dbab90/downloaddb35c60415ba6b4d102945a5b73c8000MD56THUMBNAILConvergtheoremultinomisaturandlogimodels.pdf.jpgConvergtheoremultinomisaturandlogimodels.pdf.jpgGenerated Thumbnailimage/jpeg1395https://bonga.unisimon.edu.co/bitstreams/4274b48d-5771-4899-9403-4823eebf0242/downloadf292dbc9fd72e87ea76664875ec8fb06MD55PDF.pdf.jpgPDF.pdf.jpgGenerated Thumbnailimage/jpeg3773https://bonga.unisimon.edu.co/bitstreams/5b7b0f70-367a-4d8a-bde2-8543eb7937d9/download1038a1e7ca88333738c96c4c100c34b8MD5720.500.12442/6233oai:bonga.unisimon.edu.co:20.500.12442/62332024-08-14 21:52:41.595http://creativecommons.org/licenses/by-nc-nd/4.0/Attribution-NonCommercial-NoDerivatives 4.0 Internacionalopen.accesshttps://bonga.unisimon.edu.coRepositorio Digital Universidad Simón Bolívarrepositorio.digital@unisimon.edu.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 |