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...

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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
Description
Summary: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.