The logit function is an important part of
logistic regression: for more information, please see that article.In
mathematics, especially as applied in
statistics, the logit (pronounced with a long "o" and a soft "g",
IPA ) of a number p between 0 and 1 is (The base of the
logarithm function used here is of little importance in the present article, as long as it is greater than 1, but the
natural logarithm with base
e is often used.) 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 (OR), thus providing an additive mechanism for combining odds-ratios:
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In the logit regression model, the predicted values for the
dependent or response variable will never be less than (or equal to) 0, or greater than (or equal to) 1, regardless of the values of the independent variables;it is, therefore, commonly used to analyze binary dependent or response variables (see also the
binomial distribution ).This is accomplished by applying the following regression equation (the term logit was first used by Berkson, 1944):
y=exp(b0 +b1*x1 + ... + bn*xn)/{1+exp(b0 +b1*x1 + ... + bn*xn)}
One can easily recognize that,regardless of the regression coefficients or the magnitude of the x values,this model will always produce predicted values (predicted y's) in the range of 0 to 1.The name logit stems from the fact that one can easily linearize this model via the logit transformation. Suppose we think of the binary dependent variable y in terms of an underlying continuous probability p,ranging from 0 to 1.We can then transform that probability p as:
p' = loge{p/(1-p)}
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