Logit Link Function

The logit link transforms a probability into the log of the odds ratio. The odds ratio is the ratio of the predicted probability of the positive to the predicted probability of the negative class. The log of the odds ratio has the appropriate range.

The odds ratio is a measure of the evidence for or against the positive target class. Odds ratios can be associated with particular predictor value. Odds ratios are naturally multiplicative, which makes the log of odds ratios additive. The log-odds ratio interprets the influence of a predictor as additive evidence for or against the positive class.

An advantage of the logit link is that the training data can be sampled independently from the two classes. This can be very significant in cases in which one class is rare or costly, such as the instances of a disease. Analysis of disease factors can be done directly from a sample of healthy people and a sample of people with the disease. This type of sampling is known as retrospective sampling.

For logistic regression, the logit link is the default. For technical reasons, this link is called the canonical link.