geometricffMlink {VGAMextra} | R Documentation |
Link functions for the mean of 1–parameter discrete distributions: The Geometric Distribution.
Description
Computes the geometricffMlink
transformation, including its inverse
and the first two derivatives.
Usage
geometricffMlink(theta, bvalue = NULL, inverse = FALSE,
deriv = 0, short = TRUE, tag = FALSE)
Arguments
theta |
Numeric or character. See below for further details. |
bvalue , inverse , deriv , short , tag |
Details at |
Details
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.,
Here, is the probability of succes, as in
geometric
.
While this link function can be used to model any parameter lying in
, it is particularly useful for event-rate geometric data
where the mean can be written in terms of some rate of events,
say
, as
and the time (as
) can be easily
incorporated in the analysis as an offset.
Under this link function the domain set for
is
. Hence, values of
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.
Value
For deriv = 0
, the geometricffMlink
transformation of
theta
when inverse = FALSE
. When
inverse = TRUE
then theta
becomes , 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.
Warning
Numerical instability may occur if covariates are used leading to
values of out of range. Try to overcome this by using
argument
bvalue
.
Note
This function may return Inf
of -Inf
for values of
too close to
and
respectively.
Author(s)
V. Miranda and T. W. Yee
See Also
geometric
,
Links
,
logitlink
,
logffMlink
.
Examples
### 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)