Logitlogodds

Logitlogodds is not a standard, widely recognized term in statistics. In ordinary usage, the log-odds of a probability p in (0,1) is defined as the natural logarithm of the odds: log-odds = log(p/(1−p)). This quantity is also called the logit of p, and it forms the core of logistic models because it maps probabilities to the real line in a monotone way.

Because logitlogodds is not a fixed technical term, it can be encountered as shorthand for several related ideas or, less often, as a nonstandard composite transform. Possible interpretations include: (1) the logit of a probability p itself, i.e., log(p/(1−p)); (2) the natural logarithm of the odds, which is the same as the logit; or (3) the natural logarithm of the log-odds value, i.e., log(log(p/(1−p))). Of these, interpretation (3) requires p > 0.5 for the log-odds to be positive, since log(·) requires a positive input; interpretation (1)/ (2) are identical.

If one encounters the term in practice, note the domain and interpretation. log(p/(1−p)) maps p in (0,1) to the entire real line, while log(log(p/(1−p))) is defined only when p > 0.5 and yields negative values when p is near 0.5 from above. The additional nesting tends to complicate interpretation and is rarely used in standard inference, though it may arise in exploratory data analysis or in special modeling contexts.

Related concepts include the logit function, odds, and logistic regression. See also probit models and transformations of probabilities to the real line.