loglog | R Documentation |
This is the log-log link function for generalized linear models.
loglog
An object of class link-glm
of length 5.
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.
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.
# 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)
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