inv_logit() [4/8]

double stan::math::inv_logit ( double  a )

inline

Returns the inverse logit function applied to the argument.

The inverse logit function is defined by

$\mbox{logit}^{-1}(x) = \frac{1}{1 + \exp(-x)}$.

This function can be used to implement the inverse link function for logistic regression.

The inverse to this function is logit.

$$\mbox{inv\_logit}(y) = \begin{cases} \mbox{logit}^{-1}(y) & \mbox{if } -\infty\leq y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } y = \textrm{NaN} \end{cases}$$

$$\frac{\partial\, \mbox{inv\_logit}(y)}{\partial y} = \begin{cases} \frac{\partial\, \mbox{logit}^{-1}(y)}{\partial y} & \mbox{if } -\infty\leq y\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } y = \textrm{NaN} \end{cases}$$

$$\mbox{logit}^{-1}(y) = \frac{1}{1 + \exp(-y)}$$

$$\frac{\partial \, \mbox{logit}^{-1}(y)}{\partial y} = \frac{\exp(y)}{(\exp(y)+1)^2}$$

Parameters

a

Argument.

Returns

Inverse logit of argument.

Definition at line 51 of file inv_logit.hpp.