The Measure of Fit and Cut-Off Point for a Binomial Logit Model. an Overlooked Contribution of Jan Salomon Cramer
Abstract
Research background
This paper revisits the contribution of Jan Salomon (Mars) Cramer (1928–2014) to binomial logit modelling. Cramer proposed both a novel measure of fit for binomial logit models and a cut-off point for binary classification, particularly suitable for unbalanced samples.
Purpose
To present and demonstrate J.S. Cramer’s often-overlooked proposals for a new measure of fit and a cut-off point in binomial logit models. Additionally, the paper discusses the relevance of Cramer’s contributions in the current discourse on binomial logit modelling.
Research methodology
The study is based on a literature analysis aimed at establishing the current state of knowledge regarding J.S. Cramer’s contributions to binomial logit modelling, including the citation analysis using Scopus.
Results
We highlight that the measure of fit proposed by Cramer in 1999, known as Cramer’s lambda, has gained recognition in the literature under a different name – Tjur’s D – introduced a decade later (2009). We also note that Cramer’s proposed cut-off point, alpha, is rarely cited as an alternative to more commonly referenced thresholds. These arguments are illustrated with a numerical example.
Novelty
Both of J.S. Cramer’s proposals remain relatively unknown today. We hope this paper contributes to re-establishing Mars Cramer’s legacy in econometrics. Cramer’s lambda and Cramer’s alpha deserve recognition and adoption as legitimate standards for binomial logit modelling.
© 2026 Marek Gruszczyński, published by University of Szczecin
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