Inverses of link functions

A collection of the inverses of the link functions for the potential impact fraction.

Usage

inv_logit(x)

inv_log_complement(x)

inv_hawkins(x)

Arguments

x

A value such that inv_link(x) is a potential impact fraction or a population attributable fraction.

Details

The functions programmed are as follows

$$ \text{inv\_logit}(\text{PIF}) = \dfrac{ 1 }{ 1 + \exp(-x) }, $$

$$ \text{inv\_log-complement}(\text{PIF}) = 1 - \exp(x), $$

and

$$ \text{inv\_Hawkins}(\text{PIF}) = \frac{1}{2} \exp(-x) \cdot \big(\exp(x) - 1\big) \cdot \big(\exp(x) + 1\big) $$

See also

linkfuns for the definition of the link functions and deriv_linkfuns for their derivatives.