Description Usage Arguments Details Value Author(s) See Also Examples

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

1 2 3 4 | ```
cloglog(p)
invcloglog(x)
invloglog(x)
loglog(p)
``` |

`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. |

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.

`cloglog`

returns `x`

,
`invcloglog`

and `invloglog`

return probability `p`

,
and `loglog`

returns `x`

.

Statisticat, LLC. [email protected]

1 2 3 4 | ```
library(LaplacesDemon)
x <- -5:5
p <- invloglog(x)
x <- loglog(p)
``` |

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