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 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.

• Autores: Orozco-Acosta, Erick; Llinás-Solano, Humberto; Fonseca-Rodríguez, Javier
• 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