0120-1751

S0120-17512006000200007

05 12 2006

29 2 239 265

Precisiones en la teoría de los modelos logísticos

Accuracies in the Theory of the Logistic Models

HUMBERTO JESÚS LLINÁS¹

¹Universidad del Norte, Barranquilla, Colombia, Profesor. E-mail: hllinas@uninorte.edu.co

Resumen

]]> 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.

Abstract

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.

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