| fsqrt {VGAM} | R Documentation |
Computes the folded square root transformation, including its inverse and the first two derivatives.
fsqrt(theta, earg = list(min=0, max=1, mux=sqrt(2)),
inverse = FALSE, deriv = 0, short = TRUE, tag = FALSE)
theta |
Numeric or character.
See below for further details.
|
earg |
List with components min, max and mux.
These are called L, U and K below.
|
inverse |
Logical. If TRUE the inverse function is computed.
|
deriv |
Order of the derivative. Integer with value 0, 1 or 2.
|
short |
Used for labelling the blurb slot of a
vglmff-class object.
|
tag |
Used for labelling the linear/additive predictor in the
initialize slot of a vglmff-class object.
Contains a little more information if TRUE.
|
The folded square root link function can be applied to
parameters that lie between L and U inclusive.
Numerical values of theta
out of range result in NA or NaN.
The arguments short and tag are used only if
theta is character.
For fsqrt with deriv = 0:
K *
(sqrt(theta-L) - sqrt(U-theta))
or
mux * (sqrt(theta-min) - sqrt(max-theta))
when inverse = FALSE,
and if inverse = TRUE then some more
complicated function that returns a NA unless
theta is between -mux*sqrt(max-min) and
mux*sqrt(max-min).
For deriv = 1, then the function returns
d theta / d eta as a function of theta
if inverse = FALSE,
else if inverse = TRUE then it returns the reciprocal.
The default has, if theta is 0 or 1, the link function
value is -sqrt(2) and +sqrt(2) respectively.
These are finite values, therefore one cannot use this link function for
general modelling of probabilities because of numerical problem,
e.g., with binomialff, cumulative. See
the example below.
Thomas W. Yee
p = seq(0.01, 0.99, by=0.01)
fsqrt(p)
max(abs(fsqrt(fsqrt(p), inverse=TRUE) - p)) # Should be 0
p = c(seq(-0.02, 0.02, by=0.01), seq(0.97, 1.02, by=0.01))
fsqrt(p) # Has NAs
## Not run:
p = seq(0.01, 0.99, by=0.01)
par(mfrow=c(2,2))
y = seq(-4, 4, length=100)
for(d in 0:1) {
matplot(p, cbind(logit(p, deriv=d), fsqrt(p, deriv=d)),
type="n", col="purple", ylab="transformation",
lwd=2, las=1,
main=if(d==0) "Some probability link functions"
else "First derivative")
lines(p, logit(p, deriv=d), col="limegreen", lwd=2)
lines(p, probit(p, deriv=d), col="purple", lwd=2)
lines(p, cloglog(p, deriv=d), col="chocolate", lwd=2)
lines(p, fsqrt(p, deriv=d), col="tan", lwd=2)
if(d==0) {
abline(v=0.5, h=0, lty="dashed")
legend(0, 4.5, c("logit", "probit", "cloglog", "fsqrt"),
col=c("limegreen","purple","chocolate", "tan"), lwd=2)
} else
abline(v=0.5, lty="dashed")
}
for(d in 0) {
matplot(y, cbind(logit(y, deriv=d, inverse=TRUE),
fsqrt(y, deriv=d, inverse=TRUE)),
type="n", col="purple", xlab="transformation", ylab="p",
lwd=2, las=1,
main=if(d==0) "Some inverse probability link functions"
else "First derivative")
lines(y, logit(y, deriv=d, inverse=TRUE), col="limegreen", lwd=2)
lines(y, probit(y, deriv=d, inverse=TRUE), col="purple", lwd=2)
lines(y, cloglog(y, deriv=d, inverse=TRUE), col="chocolate", lwd=2)
lines(y, fsqrt(y, deriv=d, inverse=TRUE), col="tan", lwd=2)
if(d==0) {
abline(h=0.5, v=0, lty="dashed")
legend(-4, 1, c("logit", "probit", "cloglog", "fsqrt"),
col=c("limegreen","purple","chocolate", "tan"), lwd=2)
}
}
## End(Not run)
# This is lucky to converge
earg = list(min=0, max=1, mux=5)
data(hunua)
fit.h = vglm(agaaus ~ bs(altitude),
fam= binomialff(link="fsqrt", earg=earg),
data=hunua, trace=TRUE, crit="d")
## Not run:
plotvgam(fit.h, se=TRUE, lcol="red", scol="red",
main="Red is Hunua, Blue is Waitakere")
## End(Not run)
predict(fit.h, hunua, type="response")[1:3]
## Not run:
# The following fails.
data(pneumo)
pneumo = transform(pneumo, let=log(exposure.time))
earg = list(min=0, max=1, mux=10)
fit = vglm(cbind(normal, mild, severe) ~ let,
cumulative(link="fsqrt", earg=earg, par=TRUE, rev=TRUE),
data = pneumo, trace=TRUE, maxit=200)
## End(Not run)