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) powl(x <- 1:5) 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 powl(x <- (-5):5, 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, beta.ab(lshape1="powl", lshape2="powl", eshape1=list(power=0.5), eshape2=list(power=0.5), i1=3, i2=7)) t(coef(fit, matrix=TRUE)) Coef(fit) # Useful for intercept-only models vcov(fit, untrans=TRUE)