powerlink: Power Link Function

Description

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

Usage

powerlink(theta, power = 1, inverse = FALSE, deriv = 0,
          short = TRUE, tag = FALSE)

Arguments

theta

Numeric or character. See below for further details.

power

This denotes the power or exponent.

inverse, deriv, short, tag

Details at Links.

Value

For powerlink 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.

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.

Examples

Run this code

powerlink("a", power = 2, short = FALSE, tag = TRUE)
powerlink(x <- 1:5)
powerlink(x, power = 2)
max(abs(powerlink(powerlink(x, power = 2),
                  power = 2, inverse = TRUE) - x))  # Should be 0
powerlink(x <- (-5):5, power = 0.5)  # Has NAs

# 1/2 = 0.5
pdata <- data.frame(y = rbeta(n = 1000, shape1 = 2^2, shape2 = 3^2))
fit <- vglm(y ~ 1, beta.ab(lshape1 = powerlink(power = 0.5), i1 = 3,
                           lshape2 = powerlink(power = 0.5), i2 = 7), pdata)
t(coef(fit, matrix = TRUE))
Coef(fit)  # Useful for intercept-only models
vcov(fit, untransform = TRUE)