- Logit
:"The logit function is an important part of
logistic regression : for more information, please see that article."The logit function is the inverse of the "sigmoid", or "logistic" function used in
mathematics , especially instatistics . The logit of a number "p" between 0 and 1 is given by the formula::
Logit is pronEng|ˈloʊdʒɪt with a long "o" and a soft "g".
The base of the
logarithm function used is of little importance in the present article, as long as it is greater than 1, but thenatural logarithm with base e is the one most often used.If "p" is a
probability then "p"/(1 − "p") is the correspondingodds , and the logit of the probability is the logarithm of the odds; similarly the difference between the logits of two probabilities is the logarithm of theodds ratio ("R"), thus providing a shorthand for writing the correct combination of odds-ratios only by adding and subtracting::
History
The logit model was introduced by
Joseph Berkson in1944 , who coined the term. The term was borrowed by analogy from the very similarprobit model developed byChester Ittner Bliss in 1934.G. A. Barnard in1949 coined the commonly used term "log-odds"; the log-odds of an event is the logit of the probability of the event.Uses and properties
* The logit in logistic regression is a special case of a link function in a
generalized linear model : it is the canonicallink function for thebinomial distribution .
* The logit function is the negative of thederivative of thebinary entropy function .
* The logit is also central to the probabilisticRasch model formeasurement , which has applications in psychological and educational assessment, among other areas.See also
*
Daniel McFadden , a Nobel Prize winner for development of a particular logit model used in economics
* Logit analysis in marketing
*Perceptron
*Probit
*Logistic regression
*Logistic function External links
* [http://www.cambridge.org/resources/0521815886/1208_default.pdf Origins and development of the logit model]
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