logitnr: Logit link with a natural response parameter.

In trobinj/trtools: Miscellaneous Tools for Teaching Statistics

Logit link with a natural response parameter.

Description

Link function for logistic regression models with a (fixed/known) natural response parameter.

Usage

logitnr(nrp = 0)

Arguments

nrp	Natural response parameter in [0,1).

Details

The logit link function with a natural response parameter is defined as log((E(Y) - \pi)/(1 - E(Y)) and inverse link function E(Y) = \pi + (1 - \pi)/(1 + exp(-\eta)), where 0 \le \pi < 1 is the natural response parameter. Note that the usual logit link function is a special case where \pi = 0. The link function implies a lower asymptote of \pi for E(Y) as \eta approaches negative infinity.

Note

User-specified starting values for the regression parameters may be required in cases where \pi is substantially larger than zero. One strategy is to obtain these from a model with a smaller value \pi.

See Also

logitnnr

Examples

# obtain starting values with the natural response parameter set to 0
tmp <- glm(cbind(total-y, y) ~ density + species, 
 family = binomial(link = logitnr(0)), data = rotifer)
# use starting values with a fixed natural response parameter of 0.1
glm(cbind(total-y, y) ~ density + species, 
 family = binomial(link = logitnr(0.1)), data = rotifer, start = coef(tmp))

trobinj/trtools documentation built on Jan. 3, 2025, 4:14 a.m.