Published

2020-07-01

Convergence Theorems in Multinomial Saturated and Logistic Models

Teoremas de convergencias en los modelos saturados y logísticos multinomiales

DOI:

https://doi.org/10.15446/rce.v43n2.79151

Keywords:

Multinomial logit model, Saturated model, Logistic regression, Maximum likelihood estimator, Score vector, Fisher information matrix (en)
Modelo logístico multinomial, Modelo saturado, Regresión logística, Estimador de máxima verosimilitud, Vector score, Matriz de información de Fisher (es)

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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.

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.

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How to Cite

APA

Orozco-Acosta, E., LLinás-Solano, H. and Fonseca-Rodríguez, J. (2020). Convergence Theorems in Multinomial Saturated and Logistic Models. Revista Colombiana de Estadística, 43(2), 211–231. https://doi.org/10.15446/rce.v43n2.79151

ACM

[1]
Orozco-Acosta, E., LLinás-Solano, H. and Fonseca-Rodríguez, J. 2020. Convergence Theorems in Multinomial Saturated and Logistic Models. Revista Colombiana de Estadística. 43, 2 (Jul. 2020), 211–231. DOI:https://doi.org/10.15446/rce.v43n2.79151.

ACS

(1)
Orozco-Acosta, E.; LLinás-Solano, H.; Fonseca-Rodríguez, J. Convergence Theorems in Multinomial Saturated and Logistic Models. Rev. colomb. estad. 2020, 43, 211-231.

ABNT

OROZCO-ACOSTA, E.; LLINÁS-SOLANO, H.; FONSECA-RODRÍGUEZ, J. Convergence Theorems in Multinomial Saturated and Logistic Models. Revista Colombiana de Estadística, [S. l.], v. 43, n. 2, p. 211–231, 2020. DOI: 10.15446/rce.v43n2.79151. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/79151. Acesso em: 28 mar. 2024.

Chicago

Orozco-Acosta, Erick, Humberto LLinás-Solano, and Javier Fonseca-Rodríguez. 2020. “Convergence Theorems in Multinomial Saturated and Logistic Models”. Revista Colombiana De Estadística 43 (2):211-31. https://doi.org/10.15446/rce.v43n2.79151.

Harvard

Orozco-Acosta, E., LLinás-Solano, H. and Fonseca-Rodríguez, J. (2020) “Convergence Theorems in Multinomial Saturated and Logistic Models”, Revista Colombiana de Estadística, 43(2), pp. 211–231. doi: 10.15446/rce.v43n2.79151.

IEEE

[1]
E. Orozco-Acosta, H. LLinás-Solano, and J. Fonseca-Rodríguez, “Convergence Theorems in Multinomial Saturated and Logistic Models”, Rev. colomb. estad., vol. 43, no. 2, pp. 211–231, Jul. 2020.

MLA

Orozco-Acosta, E., H. LLinás-Solano, and J. Fonseca-Rodríguez. “Convergence Theorems in Multinomial Saturated and Logistic Models”. Revista Colombiana de Estadística, vol. 43, no. 2, July 2020, pp. 211-3, doi:10.15446/rce.v43n2.79151.

Turabian

Orozco-Acosta, Erick, Humberto LLinás-Solano, and Javier Fonseca-Rodríguez. “Convergence Theorems in Multinomial Saturated and Logistic Models”. Revista Colombiana de Estadística 43, no. 2 (July 1, 2020): 211–231. Accessed March 28, 2024. https://revistas.unal.edu.co/index.php/estad/article/view/79151.

Vancouver

1.
Orozco-Acosta E, LLinás-Solano H, Fonseca-Rodríguez J. Convergence Theorems in Multinomial Saturated and Logistic Models. Rev. colomb. estad. [Internet]. 2020 Jul. 1 [cited 2024 Mar. 28];43(2):211-3. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/79151

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