Logistic regression: Difference between revisions

Revision as of 14:43, 5 February 2024

Revision as of 20:45, 25 February 2024

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In the 1930s, the [[probit model]] was developed and systematized by [[Chester Ittner Bliss]], who coined the term "probit" in {{harvtxt|Bliss|1934}}, and by [[John Gaddum]] in {{harvtxt|Gaddum|1933}}, and the model fit by [[maximum likelihood estimation]] by [[Ronald A. Fisher]] in {{harvtxt|Fisher|1935}}, as an addendum to Bliss's work. The probit model was principally used in [[bioassay]], and had been preceded by earlier work dating to 1860; see {{slink|Probit model|History}}. The probit model influenced the subsequent development of the logit model and these models competed with each other.{{sfn|Cramer|2002|p=7–9}}

The logistic model was likely first used as an alternative to the probit model in bioassay by [[Edwin Bidwell Wilson]] and his student [[Jane Worcester]] in {{harvtxt|Wilson|Worcester|1943}}.{{sfn|Cramer|2002|p=9}} However, the development of the logistic model as a general alternative to the probit model was principally due to the work of [[Joseph Berkson]] over many decades, beginning in {{harvtxt|Berkson|1944}}, where he coined "logit", by analogy with "probit", and continuing through {{harvtxt|Berkson|1951}} and following years.<ref>{{harvnb|Cramer|2002|p=8|ps=, "As far as I can see the introduction of the logistics as an alternative to the normal probability function is the work of a single person, Joseph Berkson (1899–1982), ..."}}</ref> The logit model was initially dismissed as inferior to the probit model, but "gradually achieved an equal footing with the logitprobit",{{sfn|Cramer|2002|p=11}} particularly between 1960 and 1970. By 1970, the logit model achieved parity with the probit model in use in statistics journals and thereafter surpassed it. This relative popularity was due to the adoption of the logit outside of bioassay, rather than displacing the probit within bioassay, and its informal use in practice; the logit's popularity is credited to the logit model's computational simplicity, mathematical properties, and generality, allowing its use in varied fields.{{sfn|Cramer|2002|p=10–11}}

Various refinements occurred during that time, notably by [[David Cox (statistician)|David Cox]], as in {{harvtxt|Cox|1958}}.<ref name=wal67est>{{cite journal|last1=Walker|first1=SH|last2=Duncan|first2=DB|title=Estimation of the probability of an event as a function of several independent variables|journal=Biometrika|date=1967|volume=54|issue=1/2|pages=167–178|doi=10.2307/2333860|jstor=2333860}}</ref>