Once Again in Defense of Logit (Log Odds)
The Birth (1944) - in the Shadow of Probit - The Triumph
The term “logit” was coined by Joseph Berkson in 1944, by analogy to the “probit”. Though, a related term “logistic function” appeared much earlier. It was invented in 1838 by the Belgian mathematician Verhulst to describe population growth. Later it was used in modeling autocatalytic chemical reactions and in bioassays (see, for example, Cramer (2003)). According to Cramer (2003):
“As far as I can see the introduction of the logistic as an alternative to the normal probability function is the work of a single person, namely Berkson... The issue of logit versus probit was tangled by Berkson’s simultaneous attacks on the method of maximum likelihood and his advocacy of minimum chi-squared estimation instead... it was Berkson who persisted and fought a long and spirited campaign which lasted for several decades ...Berkson’s case for the logit was not helped by his simultaneous attacks on the established wisdom of maximum likelihood estimation and his advocacy of minimum chi-squared. The unpleasant atmosphere in which this discussion was conducted can be gauged from the acrimonious exchanges between R.A. Fisher and Berkson in Fisher (1954).”
Said above explains why logit was waiting for its recognition in statistical community for such a long time.
From Jaynes (2003) we can learn about some unsuccessful attempts to introduce other names for logit: “deciban” (Allan Turing in 1941 in classified cryptographic work in England during World War II to decipher Nazi’s “Enigma”); “lods” (I.J. Good in 1950); and “evidence” (E.T. Jaynes in 1956).
Also, it should be noticed that there exists an additional, very interesting and rather surprising interpretation of logit in terms of the general system theory. In accordance with Voit and Knapp (1997), logistic model in epidemiological context is a natural and essential consequence of the formulation of a disease process as the dynamic model in a S-system form. The corresponding S-system of ordinary nonlinear differential equations describes epidemic development in time while logistic regression characterizes epidemic steady state. We mentioned this fact in our early work, Shtatland and Barton (1998). Summarizing, we can see that logit does have meaningful interpretations in various, seemingly different fields.
References
Allison, P.D. (2017) “In Defense of Logit – Part 1”, https://statisticalhorizons.com/in-defense-of-logit-part-1
Cramer, J.S. (2003) “The origins and development of the logit model”, Cambridge University Press, pp.10 – 11. https://pdfs.semanticscholar.org/7218/daab6499b46759f0a16d173d01d348bed906.pdf
Jaynes E. T. (2003) “Probability Theory: The Logic of Science”, Cambridge University Press: New York.
Shtatland, E.S. (2019) “Logistic Regression and Information Theory: Part 1 - Do log odds have any intuitive meaning?” https://statisticalmiscellany.blogspot.com/2019/09/logistic-regression-and-information.html
Shtatland, E.S. and Barton M.B. (1998) “Information Theory Makes Logistic Regression Special”. NESUG Proceedings
Voit, E. O. and Knapp, R. G. (1997). Derivation of the linear-logistic model and Cox’s proportional hazard model from a canonical system description. Statistics in Medicine, 16, 1705-1729
