VGAM (version 0.9-6)

rhobit: Rhobit Link Function

Description

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

Usage

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

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

inverse, deriv, short, tag

Details at Links.

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

Details

The rhobit 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.

References

Documentation accompanying the VGAM package at http://www.stat.auckland.ac.nz/~yee contains further information and examples.

See Also

Links, binom2.rho, fisherz.

Examples

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