Statistics > Methodology
[Submitted on 4 Apr 2022 (v1), last revised 2 Feb 2023 (this version, v2)]
Title:A Modification of McFadden's $R^2$ for Binary and Ordinal Response Models
View PDFAbstract: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-$R^2$, 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 $R^2$ interestingly proves quite invariant to an increasing number of response categories of an ordinal model.
Submission history
From: Ejike R. Ugba [view email][v1] Mon, 4 Apr 2022 08:17:34 UTC (1,135 KB)
[v2] Thu, 2 Feb 2023 02:57:18 UTC (3,607 KB)
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