geometricffMeanlink {VGAMextra} | R Documentation |
Computes the geometricffMeanlink
transformation, including its inverse
and the first two derivatives.
geometricffMeanlink(theta, bvalue = NULL, inverse = FALSE, deriv = 0, short = TRUE, tag = FALSE)
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 geometricffMeanlink
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
,
logit
,
logffMeanlink
.
### Example 1 ### my.probs <- ppoints(100) geol.inv <- geometricffMeanlink(theta = geometricffMeanlink(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 = geometricffMeanlink(theta = my.probs), inv.geoffl = geometricffMeanlink(theta = my.probs, inverse = TRUE)) ### Example 3 Some probability link functions ### my.probs <- ppoints(100) par(lwd = 2) plot(my.probs, logit(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, geometricffMeanlink(my.probs), col = "gray50") lines(my.probs, logffMeanlink(my.probs), col = "blue") lines(my.probs, probit(my.probs), col = "purple") lines(my.probs, cloglog(my.probs), col = "chocolate") lines(my.probs, cauchit(my.probs), col = "tan") abline(v = c(0.5, 1), lty = "dashed") abline(v = 0, h = 0, lty = "dashed") legend(0.1, 8, c("geometricffMeanlink", "logffMeanlink","logit", "probit", "cloglog", "cauchit"), col = c("gray50", "blue", "limegreen", "purple", "chocolate", "tan"), lwd = 1, cex = 0.5) par(lwd = 1)