Derivatives of link functions

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

Usage

deriv_logit(pif)

deriv_log_complement(pif)

deriv_hawkins(pif)

deriv_identity(pif)

Arguments

pif

The value of a potential impact fraction or a population attributable fraction

Details

The functions programmed are as follows

$$ \text{deriv\_logit}(\text{PIF}) = \dfrac{ 1 }{ \text{PIF} \cdot (1 - \text{PIF}) }, $$

$$ \text{deriv\_log-complement}(\text{PIF}) = \dfrac{ 1 }{ \text{PIF} - 1 }, $$

and

$$ \text{deriv\_Hawkins}(\text{PIF}) = \dfrac{ 1 }{ \sqrt{\text{PIF}^2 + 1} }, $$

See also

linkfuns for the definition of the link functions and inv_linkfuns for the inverses of the link functions.