Published

2005-01-01

ESTIMACION DE MODELOS MULTINIVEL PARA DATOS CATEGORICOS A TRAVES DE MINIMOS CUADRADOS GENERALIZADOS

ESTIMATING MULTILEVEL MODELS FOR CATEGORICAL DATA VIA GENERALIZED LEAST SQUARES

Keywords:

Modelos multinivel, mínimos cuadrados generalizados, valores singulares truncados (es)
Multilevel models, Generalized least squares, Truncated Singular Value (en)

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Authors

  • Minerva Montero Díaz Instituto de Cibernética, Matemática y Física
  • Valia Guerra Ones Instituto de Cibernética, Matemática y Física
Montero, Castell & Ojeda (2002) propusieron una estrategia para formular modelos multinivel para tablas de contingencia basada en la aplicación del modelo lineal general a datos categóricos jerárquicos. Aplicando el método a un modelo de regresión logística multinivel con datos simulados, encontramos que las estimaciones de los parámetros aleatorios son inadmisibles en ciertas situaciones, con sesgos grandes y estimaciones negativas de la varianza cuando los conjuntos de datos son desbalanceados. Para corregir los estimadores proponemos una técnica basada en descomposición de valores singulares truncados en la solución de mínimos cuadrados generalizados para estimar los parámetros aleatorios. Mediante simulación mostramos la efectividad de la técnica en cuanto a la reducción del sesgo de los estimadores.
Montero et al. (2002) proposed a strategy to formulate multilevel models related to a contingency table sample. This methodology is based on the application of the general linear model to hierarchical categorical data. In this paper we applied the method to a multilevel logistic regression model using simulated data. We find that the estimates of the random parameters are inadmissible in some circumstances; large bias and negative estimates of the variance are expected for unbalanced data sets. In order to correct the estimates we propose to use a numerical technique based on the Truncated Singular Value Decomposition (TSVD) in the solution of the problem of generalized least squares associated to the estimation of the random parameters. Finally a simulation study is presented to shows the effectiveness of this technique for reducing the bias of the estimates.

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Copyright (c) 2005 Revista Colombiana de Estadística

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