Convergence theorems in multinomial saturated and logistic models

dc.contributor.authorOrozco-Acosta, Erick
dc.contributor.authorLlinás-Solano, Humberto
dc.contributor.authorFonseca-Rodríguez, Javier
dc.description.abstractIn 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.eng
dc.description.abstractEn 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
dc.publisherUniversidad Nacional de Colombiaspa
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional
dc.sourceRevista Colombiana de Estadística - Theoretical Statisticsspa
dc.sourceVol. 43, N° 2, (2020)
dc.subjectMultinomial logit modeleng
dc.subjectSaturated modeleng
dc.subjectLogistic regressioneng
dc.subjectMaximum likelihood estimatoreng
dc.subjectScore vectoreng
dc.subjectFisher information matrixeng
dc.subjectModelo logístico multinomialeng
dc.subjectModelo saturadospa
dc.subjectRegresión logísticaspa
dc.subjectEstimador de máxima verosimilitudspa
dc.subjectVector scorespa
dc.subjectMatriz de información de Fisherspa
dc.titleConvergence theorems in multinomial saturated and logistic modelseng
dc.title.translatedTeoremas de convergencias en los modelos saturados y logísticos multinomialesspa
dc.type.spaArtículo científicospa
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