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

Computes the `geometricffMlink`

transformation, including its inverse
and the first two derivatives.

1 2 |

`theta` |
Numeric or character. See below for further details. |

`bvalue, inverse, deriv, short, tag` |
Details at |

This is a natural link function to model the mean of the (discret)
geometric distribution, `geometric`

,
defined as the logarithmm of its mean, i.e.,

*
η = - log (prob / (1 - prob)) = -logit(prob).
*

Here, *prob* is the probability of succes, as in
`geometric`

.

While this link function can be used to model any parameter lying in
*(0, 1)*, it is particularly useful for event-rate geometric data
where the mean can be written in terms of some rate of events,
say *λ(x)*, as

*μ = λ(x) t ,*

and the time *t* (as *log(t)*) can be easily
incorporated in the analysis as an offset.

Under this link function the domain set for *prob*
is *(0, 1)*. Hence, values of *rho* too
close to the extremes, or out of range will result
in `Inf`

, `-Inf`

, `NA`

or `NaN`

.
Use argument `bvalue`

to adequately replace them before
computing the link function.

If `theta`

is a character, arguments `inverse`

and
`deriv`

are disregarded.

For `deriv = 0`

, the `geometricffMlink`

transformation of
`theta`

when `inverse = FALSE`

. When
`inverse = TRUE`

then `theta`

becomes *η*, and
`exp(-theta) / (exp(-theta) - 1)`

is returned.

For `deriv = 1`

, *d* `eta`

/ *d* `theta`

,
if `inverse = FALSE`

, else
the reciprocal *d* `theta`

/ *d* `eta`

as a function of `theta`

.

For `deriv = 2`

the second order derivatives
are correspondingly returned.

Numerical instability may occur if covariates are used leading to
values of *prob* out of range. Try to overcome this by using
argument `bvalue`

.

This function may return `Inf`

of `-Inf`

for values of
*prob* too close to *0* and *1* respectively.

V. Miranda and T. W. Yee

`geometric`

,
`Links`

,
`logitlink`

,
`logffMlink`

.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 | ```
### Example 1 ###
my.probs <- ppoints(100)
geol.inv <-
geometricffMlink(theta = geometricffMlink(theta = my.probs), # the inverse
inverse = TRUE) - my.probs
summary(geol.inv) ## zero
### Example 2. Special values of 'prob' ###
my.probs <- c(-Inf, -2, -1, 0, 0.25, 0.75, 1.0, 5, Inf, NaN, NA)
rbind(probs = my.probs,
geoffMlink = geometricffMlink(theta = my.probs),
inv.geoffl = geometricffMlink(theta = my.probs, inverse = TRUE))
### Example 3 Some probability link functions ###
my.probs <- ppoints(100)
par(lwd = 2)
plot(my.probs, logitlink(my.probs), xlim = c(-0.1, 1.1), ylim = c(-5, 8),
type = "l", col = "limegreen",
ylab = "transformation", las = 1, main = "Some probability link functions")
lines(my.probs, geometricffMlink(my.probs), col = "gray50")
lines(my.probs, logffMlink(my.probs), col = "blue")
lines(my.probs, probitlink(my.probs), col = "purple")
lines(my.probs, clogloglink(my.probs), col = "chocolate")
lines(my.probs, cauchitlink(my.probs), col = "tan")
abline(v = c(0.5, 1), lty = "dashed")
abline(v = 0, h = 0, lty = "dashed")
legend(0.1, 8,
c("geometricffMlink", "logffMlink","logitlink", "probitlink",
"clogloglink", "cauchitlink"),
col = c("gray50", "blue", "limegreen", "purple", "chocolate", "tan"),
lwd = 1, cex = 0.5)
par(lwd = 1)
``` |

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