Logit transform

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Logit transform

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The Logit transform is primarily used to transform binary response data, such as survival/non-survival or present/absent, to provide a continuous value in the range (‑,), where p is the proportion of each sample that is 1 (or 0). The inverse or back-transform is shown as p in terms of z. This transform avoids concentration of values at the ends of the range. For samples where the proportions p may approximate the values 0 or 1 (and would thus result in very large positive or negative transformed data values) a modified form of the transform may be used; this is typically achieved by adding 1/2n to the numerator and denominator, where n is the sample size. The Logit transform is often used to correct S-shaped (logistic) relationships between response and explanatory variables (see also, Logistic Regression). The standard form of the transform is:

with back transform (also known as the logistic function):

The graph below shows the form of the logit transform, which crosses the x-axis at its point of inflexion where p (or x) =0.5

Logit curve

The back- or inverse-transform yields the S-shaped logistic curve, which we have previously discussed and as shown below:

Logistic curve