Power Link Function
Computes the power transformation, including its inverse and the first two derivatives.
powerlink(theta, power = 1, inverse = FALSE, deriv = 0,
short = TRUE, tag = FALSE)theta |
Numeric or character. See below for further details. |
power |
This denotes the power or exponent. |
inverse, deriv, short, tag |
Details at |
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.
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.
Numerical problems may occur for certain combinations of
theta and power.
Consequently this link function should be used with caution.
Thomas W. Yee
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, betaR(lshape1 = powerlink(power = 0.5), i1 = 3,
lshape2 = powerlink(power = 0.5), i2 = 7), data = pdata)
t(coef(fit, matrix = TRUE))
Coef(fit) # Useful for intercept-only models
vcov(fit, untransform = TRUE)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.