In mathematics, especially as applied in statistics, the logit (pronounced with a long "o" and a soft "g", IPA /loʊdʒɪt/) of a number p between 0 and 1 is Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ... A graph of a bell curve in a normal distribution showing statistics used in educational assessment, comparing various grading methods. ... For information on how to read IPA transcriptions of English words see here. ...

This function is used in logistic regression. It has been suggested that Logit be merged into this article or section. ...

Plot of logit in the range 0 to 1, base is e

(The base of the logarithm function used here is of little importance in the present article, as long as it is greater than 1.) The logit function is the inverse of the "sigmoid", or "logistic" function. If p is a probability then p/(1 − p) is the corresponding odds, 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 the odds-ratio, thus providing an additive mechanism for combining odds-ratios. Image File history File links Plot of the logit function log(x/ (1-x)) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Plot of the logit function log(x/ (1-x)) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Logarithms to various bases: is to base e, is to base 10, and is to base 1. ... The logistic function or logistic curve is defined by the mathematical formula: for real parameters a, m, n, and . ... This article does not cite its references or sources. ... In probability theory and statistics the odds in favor of an event or a proposition are the quantity p / (1 − p), where p is the probability of the event or proposition. ... The odds-ratio is a statistical measure, particularly important in Bayesian statistics and logistic regression. ...

Logits are used for various purposes by statisticians. In particular there is the "logit model" of which the simplest sort is

where x_i is some quantity on which success or failure in the i-th in a sequence of Bernoulli trials may depend, and p_i is the probability of success in the i-th case. For example, x may be the age of a patient admitted to a hospital with a heart attack, and "success" may be the event that the patient dies before leaving the hospital. Having observed the values of x in a sequence of cases and whether there was a "success" or a "failure" in each such case, a statistician will often estimate the values of the coefficients a and b by the method of maximum likelihood. The result can then be used to assess the probability of "success" in a subsequent case in which the value of x is known. Estimation and prediction by this method are called logistic regression. In mathematics, a sequence is a list of objects (or events) arranged in a linear fashion, such that the order of the members is well defined and significant. ... In the theory of probability and statistics, a Bernoulli trial is an experiment whose outcome is random and can be either of two possible outcomes, called success and failure. ... Maximum likelihood estimation (MLE) is a popular statistical method used to make inferences about parameters of the underlying probability distribution of a given data set. ... It has been suggested that Logit be merged into this article or section. ...

A logistic regression model can be seen as a feedforward neural network with no hidden units.

The logit in logistic regression is a special case of a link function in generalized linear models. Another example is the probit model, which differs from the logit by a constant factor except in the tails. In statistics, a generalized linear model is a model relating the expected value E(y) of a dependent variable y to one or more independent variables x1, ..., xn, with the relation stated as follows. ... In statistics the generalized linear model (GLM) generalizes of the general linear model in the following ways: Error distributions from the exponential family, besides the normal distribution are permitted. ... In probability theory and statistics the probit function is the inverse cumulative distribution function, or quantile function of the normal distribution. ...

The concept of a logit is also central to the probabilistic Rasch model for measurement, which has applications in psychological and educational assessment, among other areas. Rasch models are probabilistic measurement models which find their application primarily in psychological and attainment assessment, and are being increasingly used in other areas, including the health profession. ... Various meters Measurement is the estimation or determination of extent, dimension or capacity, usually in relation to some standard or unit of measurement. ...

The logit model was introduced by Joseph Berkson in 1944, who coined the term. The term was borrowed by analogy from the very similar probit model developed by Chester Bliss in 1934. G. A. Barnard in 1949 coined the commonly used term log-odds; the log-odds of an event is the logit of the probability of the event. 1944 (MCMXLIV) was a leap year starting on Saturday (the link is to a full 1944 calendar). ... In probability theory and statistics the probit function is the inverse cumulative distribution function, or quantile function of the normal distribution. ... 1949 (MCMXLIX) was a common year starting on Saturday (the link is to a full 1949 calendar). ...

See also

• Daniel McFadden, winner of the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel for development of a particular logit model used in economics
• Logistic function
• Logit analysis in marketing
• Perceptron

Daniel L. McFadden (born July 29, 1937) is an econometrician who won (jointly with James Heckman) the 2000 Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel for his development of theory and methods for analyzing discrete choice. He is currently the E. Morris Cox Professor of... The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel (in Swedish Sveriges Riksbanks pris i ekonomisk vetenskap till Alfred Nobels minne), is a prize awarded each year for outstanding intellectual contributions in the field of economics. ... Logistic curve, specifically the sigmoid function A logistic function or logistic curve models the S-curve of growth of some set P. The initial stage of growth is approximately exponential; then, as competition arises, the growth slows, and at maturity, growth stops. ... Logit analysis is a mathematical technique used by marketers to assess the scope of customer acceptance of a product, particularly a new product. ... The perceptron is a type of artificial neural network invented in 1957 at the Cornell Aeronautical Laboratory by Frank Rosenblatt. ...

External links

• "Origins and development of the logit model" http://www.cambridge.org/resources/0521815886/1208_default.pdf