VGAM (version 0.8-1)

rhobit: Rhobit Link Function

Description

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

Usage

rhobit(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 func

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, 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. The arguments short and tag are used only if theta is character.

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, earg=list(bminvalue= -1 + .Machine$double.eps,
                    bmaxvalue=  1 - .Machine$double.eps))  # Has no NAs