inv_logit() maps finite real values to probabilities. Mathematically the
range is (0, 1), although floating-point results can round to 0 or 1
for extreme finite inputs. It is used by temperature scaling and by the
parametric calibrators fitted with logistic regression.
Details
The inverse logit, also called the logistic function, is
$$\operatorname{logit}^{-1}(x) = \frac{1}{1 + \exp(-x)}.$$
It maps real-valued scores to probabilities, is monotone increasing, and
satisfies \(\operatorname{logit}^{-1}(0) = 0.5\). The implementation uses
stats::plogis(), which evaluates the same transformation with stable
numerical handling for large positive or negative inputs. The implementation
accepts finite numeric inputs only; infinite values are rejected even though
the mathematical limits of the logistic function are defined. The returned
vector has the same length as x.
Examples
scores <- data.frame(logit_score = c(-2, -1, 0, 1, 2)) |>
dplyr::mutate(probability = inv_logit(logit_score))
scores
#> logit_score probability
#> 1 -2 0.1192029
#> 2 -1 0.2689414
#> 3 0 0.5000000
#> 4 1 0.7310586
#> 5 2 0.8807971