VGAM (version 0.8-1)

fisherz: 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 fu

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.

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.

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.

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)
plot(theta, y, type="l", las=1, ylab="", main="fisherz(theta)")
abline(v=0, h=0, lty=2)

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