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The logit transformation applies the logit function to map a probability to its log-odds. In logistic regression, the log-odds of the conditional probability of success are a linear function of the explanatory variables. For two probabilities and in , the difference of the transformed values is the natural logarithm of the odds ratio,

The transformation has an inflection point at , where its second derivative

changes sign.

The transformation has also been used to generate random numbers from the logistic map (Collins et al. 1992). If the initial value is drawn from a stationary distribution of the map with probability density function for , each transformed value has probability density function

for . Collins et al. (1992) describe this density as close to that of a normal distribution. Successive values are dependent because each value determines the next.

See also

Logistic Map, Logistic Regression, Logit Function, Odds Ratio

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References

Collins, J. J.; Fanciulli, M.; Hohlfeld, R. G.; Finch, D. C.; Sandri, G. v. H.; and Shtatland, E. S. "A Random Number Generator Based on the Logit Transform of the Logistic Variable." Computers in Physics 6, 630-632, 1992. https://doi.org/10.1063/1.168442.Pickover, C. A. Keys to Infinity. New York: Wiley, pp. 244-245, 1995.

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Logit Transformation

Cite this as:

Weisstein, Eric W. "Logit Transformation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LogitTransformation.html

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