Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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A modification of McFadden's R2 for binary and ordinal response models

  • Ejike R. Ugba (Department of Mathematics and Statistics, School of Economics and Social Sciences, Helmut Schmidt University) ;
  • Jan Gertheiss (Department of Mathematics and Statistics, School of Economics and Social Sciences, Helmut Schmidt University)
  • Received : 2022.04.01
  • Accepted : 2022.09.29
  • Published : 2023.01.31
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Abstract

A lot of studies on the summary measures of predictive strength of categorical response models consider the likelihood ratio index (LRI), also known as the McFadden-R2, a better option than many other measures. We propose a simple modification of the LRI that adjusts for the effect of the number of response categories on the measure and that also rescales its values, mimicking an underlying latent measure. The modified measure is applicable to both binary and ordinal response models fitted by maximum likelihood. Results from simulation studies and a real data example on the olfactory perception of boar taint show that the proposed measure outperforms most of the widely used goodness-of-fit measures for binary and ordinal models. The proposed R2 interestingly proves quite invariant to an increasing number of response categories of an ordinal model.

Keywords

Acknowledgement

This research was supported in part by Deutsche Forschungsgemeinschaft (DFG) through grant number GE2353/2-1.

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