ALTERNATIVE MEASURES OF THE EXPLANATORY POWER OF GENERAL MULTIVARIATE REGRESSION MODELS |
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Authors: | Martin Spiess Gerhard Tutz |
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Institution: | 1. GSOEP , DIW Berlin, Germany;2. Department of Statistics , Munich, Germany |
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Abstract: | In this paper R 2-type measures of the explanatory power of multivariate linear and categorical probit models proposed in the literature are reviewed and their deficiencies discussed. It is argued that a measure of the explanatory power should take into account the components which are explicitly modelled when a regression model is estimated while it should be indifferent to components not explicitly modelled. Based on this view three different measures for multivariate probit models are proposed. Results of a simulation study are presented, designed to compare two measures in various situations, to evaluate the BC a bootstrap technique for testing the hypothesis that the corresponding measure is zero, and to calculate approximate confidence intervals. The BC a bootstrap technique turned out to work quite well for a wide range of situations, but may lead to misleading results if the true values of the corresponding measure are close to zero. |
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Keywords: | Pseudo-R 2 Multivariate linear model Multivariate probit model Panel model Simulation study Bootstrap confidence intervals |
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