LaplacesDemon (version 16.1.0)

log-log: The log-log and complementary log-log functions

Description

The log-log and complementary log-log functions, as well as the inverse functions, are provided.

Usage

cloglog(p)
invcloglog(x)
invloglog(x)
loglog(p)

Arguments

x

This is a vector of real values that will be transformed to the interval [0,1].

p

This is a vector of probabilities p in the interval [0,1] that will be transformed to the real line.

Value

cloglog returns x, invcloglog and invloglog return probability p, and loglog returns x.

Details

The logit and probit links are symmetric, because the probabilities approach zero or one at the same rate. The log-log and complementary log-log links are asymmetric. Complementary log-log links approach zero slowly and one quickly. Log-log links approach zero quickly and one slowly. Either the log-log or complementary log-log link will tend to fit better than logistic and probit, and are frequently used when the probability of an event is small or large. A mixture of the two links, the log-log and complementary log-log is often used, where each link is weighted. The reason that logit is so prevalent is because logistic parameters can be interpreted as odds ratios.

See Also

LaplacesDemon

Examples

# NOT RUN {
library(LaplacesDemon)
x <- -5:5
p <- invloglog(x)
x <- loglog(p)
# }