Published
PRECISIONES EN LA TEORÍA DE LOS MODELOS LOGÍSTICOS
ACCURACIES IN THE THEORY OF THE LOGISTIC MODELS
Keywords:
variable de respuesta binaria, modelo lineal generalizado, teoría asintótica (es)Binary response, Generalized linear model, Asymptotic theory (en)
Downloads
1Universidad del Norte, Barranquilla, Colombia, Profesor. E-mail: hllinas@uninorte.edu.co
Se estudian los modelos logísticos, como una clase de modelos lineales generalizados (MLG). Se demuestra un teorema sobre la existencia y unicidad de las estimaciones de máxima verosimilitud (abreviadas por ML) de los parámetros logísticos y el método para calcularlas. Con base en una teoría asintótica para estas ML-estimaciones y el vector score, se encuentran aproximaciones para las diferentes desviaciones σ2 log L, siendo L la función de verosimilitud. A partir de ellas se obtienen estadísticas para distintas pruebas de hipótesis, con distribución asintótica chi-cuadrada. La teoría asintótica se desarrolla para el caso de variables independientes y no idénticamente distribuidas, haciendo las modificaciones necesarias para la conocida situación de variables idénticamente distribuidas. Se hace siempre la distinción entre datos agrupados y no agrupados.
Palabras clave: variable de respuesta binaria, modelo lineal generalizado, teoría asintótica.
The logistic models are studied, as a kind of generalized lineal models. A theorem is showed about existence and uniqueness of ML-estimates of the estimation of the logistic regression coefficients and the method in order to calculate it. According to an asymptotic theory for this ML-estimates and the score vector, it has been founded approaching for different deviations σ2 log L (in this expression, L is the function of maximum likelihood). In consequence, we have gotten statistics for different hypotheses test which is asymptotically chi-square. The asymptotic theory is developed for the independent variables and no distributed identically variables. It is made the difference between ungrouped and grouped data.
Key words: Binary response, Generalized linear model, Asymptotic theory.
Texto completo disponible en PDF
Referencias
1. Agresti, A. (1990), Categorical Data Analysis, 2nd edn, John Wiley and Sons, Inc., New York.
2. C.F,M. & McFadden, D., eds (1974),"Conditional logit analysis of qualitative choice behavior",Frontiers in Econometrics Applications, MA: MIT Press, Cambridge, pp. 105-142.
3. Dobson, A. J. (2002), An Introduction to Generalized Linear Models, 2 edn, Chapman & Hall, London.
4. Goodman, L. (1971), "The Analysis of Multidimensional Contingency Tables: Stepwise Procedures and Direct Estimation Methods for Building Models for Multiple Classifications", Technometrics (13), 33- 61.
5. Mc Cullagh, P. (1983), "Quasi-likelihood Functions", Annals of Statistics (11), 59- 67.
6. Mc Cullagh, P. & Nelder, J. (1983), Generalized Linear Models, 2 edn, Chapman and Hall, London.
7. Rao, C. (1973), Linear Statistical Inference and its Applications, 2 edn, JohnWiley and Sons, Inc., New York.
8. Theil, H. (1970), "On the Estimation of Relationships Involving Qualitative Variables", Amer. J. Sociol. (76), 103- 154.
9. Wedderburn, R. (1974), "Quasi-likelihood Functions, Generalized linear models and the Gauss-Newton Method", Biometrika (61), 439- 447.
10. Wedderburn, R. (1976), "On The Existence and Uniqueness of the Maximum Likelihood Estimates for Certain Generalized Linear Models", Biometrika (63), 27- 32.
11. Zacks, S. (1971), The Theory of Statistical Inference, 2nd edn, John Wiley and Sons Inc., New York.
How to Cite
APA
ACM
ACS
ABNT
Chicago
Harvard
IEEE
MLA
Turabian
Vancouver
Download Citation
Article abstract page views
Downloads
License
Copyright (c) 2006 Revista Colombiana de Estadística
This work is licensed under a Creative Commons Attribution 4.0 International License.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).