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

log-log {LaplacesDemon} | R Documentation

## 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.

### 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.

### Value

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

### Author(s)

Statisticat, LLC. software@bayesian-inference.com

### See Also

`LaplacesDemon`

### Examples

    library(LaplacesDemon)
    x <- -5:5
    p <- invloglog(x)
    x <- loglog(p)

[Package LaplacesDemon version 16.1.1 Index]