1\name{powerlink} 2\alias{powerlink} 3%- Also NEED an '\alias' for EACH other topic documented here. 4\title{ Power Link Function } 5\description{ 6 Computes the power transformation, including its inverse and the 7 first two derivatives. 8 9} 10\usage{ 11powerlink(theta, power = 1, inverse = FALSE, deriv = 0, 12 short = TRUE, tag = FALSE) 13} 14%- maybe also 'usage' for other objects documented here. 15\arguments{ 16 \item{theta}{ 17 Numeric or character. 18 See below for further details. 19 20 } 21 \item{power}{ 22 This denotes the power or exponent. 23 24 25 } 26 27 \item{inverse, deriv, short, tag}{ 28 Details at \code{\link{Links}}. 29 30 31 } 32 33} 34\details{ 35 The power link function raises a parameter by a certain value of 36 \code{power}. 37 Care is needed because it is very easy to get numerical 38 problems, e.g., if \code{power=0.5} and \code{theta} is 39 negative. 40 41 42 43} 44\value{ 45 For \code{powerlink} with \code{deriv = 0}, then \code{theta} raised 46 to the power of \code{power}. 47 And if \code{inverse = TRUE} then 48 \code{theta} raised to the power of \code{1/power}. 49 50 51 For \code{deriv = 1}, then the function returns 52 \emph{d} \code{theta} / \emph{d} \code{eta} as a function of \code{theta} 53 if \code{inverse = FALSE}, 54 else if \code{inverse = TRUE} then it returns the reciprocal. 55 56 57} 58%\references{ 59% McCullagh, P. and Nelder, J. A. (1989). 60% \emph{Generalized Linear Models}, 2nd ed. London: Chapman & Hall. 61% 62%} 63\author{ Thomas W. Yee } 64 65\note{ 66 Numerical problems may occur for certain combinations of 67 \code{theta} and \code{power}. 68 Consequently this link function should be used with caution. 69 70 71} 72 73\seealso{ 74 \code{\link{Links}}, 75 \code{\link{loglink}}. 76 77 78} 79\examples{ 80powerlink("a", power = 2, short = FALSE, tag = TRUE) 81powerlink(x <- 1:5) 82powerlink(x, power = 2) 83max(abs(powerlink(powerlink(x, power = 2), 84 power = 2, inverse = TRUE) - x)) # Should be 0 85powerlink(x <- (-5):5, power = 0.5) # Has NAs 86 87# 1/2 = 0.5 88pdata <- data.frame(y = rbeta(n = 1000, shape1 = 2^2, shape2 = 3^2)) 89fit <- vglm(y ~ 1, betaR(lshape1 = powerlink(power = 0.5), i1 = 3, 90 lshape2 = powerlink(power = 0.5), i2 = 7), data = pdata) 91t(coef(fit, matrix = TRUE)) 92Coef(fit) # Useful for intercept-only models 93vcov(fit, untransform = TRUE) 94} 95\keyword{math} 96\keyword{models} 97\keyword{regression} 98 99