fisherz {VGAM}R Documentation

Fisher's Z Link Function

Description

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

Usage

fisherz(theta, earg = list(), inverse = FALSE, deriv = 0,
        short = TRUE, tag = FALSE)

Arguments

theta Numeric or character. See below for further details.
earg Optional list. Extra argument for passing in additional information. Values of theta which are less than or equal to -1 can be replaced by the bminvalue component of the list earg before computing the link function value. Values of theta which are greater than or equal to 1 can be replaced by the bmaxvalue component of the list earg before computing the link function value. See Links for general information about earg.
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 fisherz link function is commonly used for parameters that lie between -1 and 1. Numerical values of theta close to -1 or 1 or out of range result in Inf, -Inf, NA or NaN. The arguments short and tag are used only if theta is character.

Value

For deriv = 0, 0.5 * log((1+theta)/(1-theta)) when inverse = FALSE, and if inverse = TRUE then (exp(2*theta)-1)/(exp(2*theta)+1).
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.
Here, all logarithms are natural logarithms, i.e., to base e.

Note

Numerical instability may occur when theta is close to -1 or 1. One way of overcoming this is to use earg.

The link function rhobit is very similar to fisherz, e.g., just twice the value of fisherz.

Author(s)

Thomas W. Yee

References

McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models, 2nd ed. London: Chapman & Hall.

See Also

Links, rhobit, logit.

Examples

theta = seq(-0.99, 0.99, by=0.01)
y = fisherz(theta)
## Not run: 
plot(theta, y, type="l", las=1, ylab="", main="fisherz(theta)")
abline(v=0, h=0, lty=2)
## End(Not run)

x = c(seq(-1.02, -0.98, by=0.01), seq(0.97, 1.02, by=0.01))
fisherz(x)  # Has NAs
fisherz(x, earg=list(bminvalue= -1 + .Machine$double.eps,
                    bmaxvalue=  1 - .Machine$double.eps))  # Has no NAs

[Package VGAM version 0.7-7 Index]