| powl {VGAM} | R Documentation |
Computes the power transformation, including its inverse and the first two derivatives.
powl(theta, earg = list(power=1), inverse = FALSE, deriv = 0,
short = TRUE, tag = FALSE)
theta |
Numeric or character.
See below for further details.
|
earg |
List. Extra argument for passing in additional information.
Here, the component name power denotes the power or exponent.
This component name should not be abbreviated.
|
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 power link function raises a parameter by a certain value of
power.
Care is needed because it is very easy to get numerical
problems, e.g., if power=0.5 and theta is
negative.
The arguments short and tag are used only if
theta is character.
For powl with deriv = 0, then theta raised
to the power of power.
And if inverse = TRUE then
theta raised to the power of 1/power.
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.
Numerical problems may occur for certain combinations of
theta and power.
Consequently this link function should be used with caution.
Thomas W. Yee
powl("a", earg=list(power=2), short=FALSE, tag=TRUE)
x = 1:5
powl(x)
powl(x, earg=list(power=2))
earg=list(power=2)
max(abs(powl(powl(x, earg=earg), earg=earg, inverse=TRUE) - x)) # Should be 0
x = (-5):5
powl(x, earg=list(power=0.5)) # Has NAs
# 1/2 = 0.5
y = rbeta(n=1000, shape1=2^2, shape2=3^2)
fit = vglm(y ~ 1, betaff(link="powl", earg=list(power=0.5), i1=3, i2=7),
trace=TRUE, cri="coef")
coef(fit, matrix=TRUE)
Coef(fit) # Useful for intercept-only models
vcov(fit, untrans=TRUE)