VGAM (version 0.7-10)

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)

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