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EL MODELO LOGÍSTICO MULTINOMIAL PARA EL CASO EN QUE LA VARIABLE DE RESPUESTA PUEDE ASUMIR UNO DE TRES NIVELES Y MODELOS RELACIONADOS
THE MULTINOMIAL LOGISTIC MODEL FOR THE CASE IN WHICH THE RESPONSE VARIABLE CAN ASSUME ONE OF THREE LEVELS AND RELATED MODELS
Keywords:
distribución binomial, logit multinomial, modelo logístico (es)Binomial distribution, Logistic model, Multinomial logit (en)
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1Universidad del Norte, División de Ciencias básicas, Departamento de Matemática y Estadística, Barranquilla, Colombia. Associate professor. Email:hllinas@uninorte.edu.co
2Corporación Universitaria Americana, Facultad de Ingeniería de Sistemas, Barranquilla, Colombia. Lecturer. Email: ccarreno@coruniamericana.edu.co
The aim of this work is to examine multinomial logistic models when the response variable can assume three levels, generalizing a previous work of logistic models with binary response variables. We also describe some related models: The null, complete, and saturated models. For each model, we present and prove some theorems concerning to the estimation of the corresponding parameters with details that we could not find in the current literature.
Key words: Binomial distribution, Logistic model, Multinomial logit.
El objetivo de este trabajo es examinar los modelos de regresión logística multinomial cuando la variable de respuesta puede asumir tres niveles, generalizando un trabajo anterior con variables respuesta binarias. También describimos algunos modelos relacionados: los modelos nulo, completo y saturado. Para cada modelo, presentamos y demostramos teoremas relacionados con la estimación de los parámetros correspondientes con detalles que no fueron posibles encontrar en la literatura.
Palabras clave: distribución binomial, logit multinomial, modelo logístico.
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References
1. Agresti, A. (1990), Categorical Data Analysis, 2 edn, John Wiley and Sons, Inc., New York.
2. Hosmer, D. & Lemeshow, S. (2000), Applied Logistic Regresssion, 2 edn, John Wiley and Sons, Inc., New York.
3. Kleinbaum, D. & Klein, M. (2002), Logistic Regression: A Self-Learning Text, 2 edn, Springer, New York.
4. Llinás, H. (2006), 'Precisiones en la teoría de los modelos logísticos', Revista Colombiana de Estadística 29(2), 239-265.
Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv35n1a08,AUTHOR = {Llinás, Humberto and Carreño, Carlos},
TITLE = {{The Multinomial Logistic Model for the Case in which the Response Variable Can Assume One of Three Levels and Related Models}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2012},
volume = {35},
number = {1},
pages = {131-138}
}
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