VGAM (version 1.1-8)

rhobitlink: Rhobit Link Function

Description

Computes the rhobit link transformation, including its inverse and the first two derivatives.

Usage

rhobitlink(theta, bminvalue = NULL, bmaxvalue = NULL,
           inverse = FALSE, deriv = 0, short = TRUE, tag = FALSE)

Value

For deriv = 0, the rhobit of theta, i.e.,

log((1 + theta)/(1 - theta)) when inverse = FALSE, and if inverse = TRUE then (exp(theta) - 1)/(exp(theta) + 1).

For deriv = 1, then the function returns d

eta / d

theta as a function of theta if inverse = FALSE, else if inverse = TRUE then it returns the reciprocal.

Arguments

theta

Numeric or character. See below for further details.

bminvalue, bmaxvalue

Optional boundary values, e.g., values of theta which are less than or equal to -1 can be replaced by bminvalue before computing the link function value. And values of theta which are greater than or equal to 1 can be replaced by bmaxvalue before computing the link function value. See Links.

inverse, deriv, short, tag

Details at Links.

Author

Thomas W. Yee

Details

The rhobitlink 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.

See Also

Links, binom2.rho, fisherz.

Examples

theta <- seq(-0.99, 0.99, by = 0.01)
y <- rhobitlink(theta)
if (FALSE) {
plot(theta, y, type = "l", ylab = "", main = "rhobitlink(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))
rhobitlink(x)  # Has NAs
rhobitlink(x, bminvalue = -1 + .Machine$double.eps,
              bmaxvalue =  1 - .Machine$double.eps)  # Has no NAs