The logit ( /ˈloʊdʒɪt/ loh-jit) function is the inverse of the sigmoidal "logistic" function used in mathematics, especially in statistics.
Log-odds and logit are synonyms[1].
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The logit of a number p between 0 and 1 is given by the formula:
The base of the logarithm function used is of little importance in the present article, as long as it is greater than 1, but the natural logarithm with base e is the one most often used.
The "logistic" function of any number is given by the inverse-logit:
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 (R), thus providing a shorthand for writing the correct combination of odds ratios only by adding and subtracting:
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 Ittner Bliss in 1934.[2] 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.