logitp

Logitp refers to the logit transform of a probability p. In statistics, the logit of p, often denoted logit(p) or logitp, is defined as log(p/(1−p)) where log is the natural logarithm. It maps p in the open interval (0, 1) to the real line (−∞, ∞). The inverse transform, returning p from a logit value, is the logistic function: p = exp(logitp) / (1 + exp(logitp)).

The logit transform is widely used as a link function in generalized linear models, particularly for binary or binomial outcomes. By modeling the logit of the probability as a linear combination of predictors, regression coefficients are interpreted as effects on the log-odds of the event of interest. This framework underpins logistic regression and related models in biostatistics, econometrics, and machine learning. The logit scale can also help stabilize variance and accommodate unbounded linear predictors, before mapping results back to a probability range.

In practical applications, p should be strictly between 0 and 1. When implementing logitp in software, exact 0 or 1 values are typically handled by clipping or adding a small epsilon to avoid division by zero or infinite values. Some environments implement the logit transform under the name logit or logitp, while others provide it as a distinct function. The concept is widely used wherever probabilities are modeled in a linear space for subsequent transformation back to probability space.