loglog: Log-log link function for generalized linear models.

In trobinj/trtools: Miscellaneous Tools for Teaching Statistics

Log-log link function for generalized linear models.

Description

This is the log-log link function for generalized linear models.

Usage

loglog

Format

An object of class link-glm of length 5.

Details

The log-log link function is defined as -log[-log[E(Y)]]. Note that using the log-log link function for the probability of "successes" is the same as using the complementary log-log link function for the probability of "failures" in a generalized linear model. The coefficients from the two models only differ by sign.

Note

Some authors define the log-log link function as log[-log[E(Y)] and the inverse link function is exp[-exp(\eta)] so that in a GLM the signs of the parameters are reversed and are equal to the parameters of a model with a complementary log-log link function for the probabilities of failures.

Examples

# the following will produce the same results up to a reversal of the sign of the coefficients
model.loglog <- glm(cbind(y, total-y) ~ density + species, 
 family = binomial(link = loglog), data = rotifer)
model.cloglog <- glm(cbind(total-y, y) ~ density + species, 
 family = binomial(link = cloglog), data = rotifer)

trobinj/trtools documentation built on Jan. 28, 2024, 3:20 a.m.