powl {VGAM}R Documentation

Power Link Function

Description

Computes the power transformation, including its inverse and the first two derivatives.

Usage

powl(theta, earg = list(power=1), inverse = FALSE, deriv = 0,
      short = TRUE, tag = FALSE)

Arguments

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.

Details

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.

Value

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.

Note

Numerical problems may occur for certain combinations of theta and power. Consequently this link function should be used with caution.

Author(s)

Thomas W. Yee

See Also

Links, loge.

Examples

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)

[Package VGAM version 0.7-7 Index]