Editing Logit (section)

== History ==
Several approaches have been explored to adapt linear regression methods to a domain where the output is a probability value <math>(0, 1)</math>, instead of any real number <math>(-\infty, +\infty)</math>. In many cases, such efforts have focused on modeling this problem by mapping the range <math>(0, 1)</math> to <math>(-\infty, +\infty)</math> and then running the linear regression on these transformed values.<ref name="Cramer2003"/>

In 1934, [[Chester Ittner Bliss]] used the cumulative normal distribution function to perform this mapping and called his model [[probit]], an abbreviation for "'''prob'''ability un'''it'''". This is, however, computationally more expensive.<ref name="Cramer2003">{{Cite web |url=http://www.cambridge.org/resources/0521815886/1208_default.pdf |title=The origins and development of the logit model |first=J. S. |last=Cramer |year=2003 |publisher=Cambridge UP |archive-url=https://web.archive.org/web/20240919043104/https://www.cambridge.org/resources/0521815886/1208_default.pdf |archive-date=19 September 2024 |url-status=dead }}</ref>

In 1944, [[Joseph Berkson]] used log of odds and called this function ''logit'', an abbreviation for "'''log'''istic un'''it'''", following the analogy for probit:
{{quote|"I use this term [logit] for <math>\ln p/q</math> following Bliss, who called the analogous function which is linear on {{tmath|x}} for the normal curve 'probit'."|Joseph Berkson (1944){{sfn|Berkson|1944|loc=p. 361, footnote 2}}}}

Log odds was used extensively by [[Charles Sanders Peirce]] (late 19th century).<ref>{{cite book |title=The history of statistics : the measurement of uncertainty before 1900 |last=Stigler |first=Stephen M. |author-link=Stephen M. Stigler |year=1986 |publisher=Belknap Press of Harvard University Press |location=Cambridge, Massachusetts |isbn=978-0-674-40340-6 |url-access=registration |url=https://archive.org/details/historyofstatist00stig }}</ref> [[G. A. Barnard]] in 1949 coined the commonly used term ''log-odds'';<ref>{{citation|title=Logistic Regression Models|first=Joseph M.|last=Hilbe|authorlink=Joseph Hilbe|publisher=CRC Press|year=2009|isbn=9781420075779|page=3|url=https://books.google.com/books?id=tmHMBQAAQBAJ&pg=PA3}}.</ref>{{sfn|Barnard|1949|p=120}} the log-odds of an event is the logit of the probability of the event.<ref>{{citation|title=Logit Models from Economics and Other Fields|first=J. S.|last=Cramer|publisher=Cambridge University Press|year=2003|isbn=9781139438193|page=13|url=https://books.google.com/books?id=1Od2d72pPXUC&pg=PA13}}.</ref> Barnard also coined the term ''lods'' as an abstract form of "log-odds",{{sfn|Barnard|1949|p=120,128}} but suggested that "in practice the term 'odds' should normally be used, since this is more familiar in everyday life".{{sfn|Barnard|1949|p=136}}