rhobit {VGAM} | R Documentation

## 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 1 can be replaced by `bmaxvalue` before computing the link function value. See `Links`.
`inverse, deriv, short, tag` | Details at `Links`.

### 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`.

### 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.

### Note

Numerical instability may occur when `theta` is close to -1 or 1. One way of overcoming this is to use `bminvalue`, etc.

The correlation parameter of a standard bivariate normal distribution lies between -1 and 1, therefore this function can be used for modelling this parameter as a function of explanatory variables.

The link function `rhobit` is very similar to `fisherz`, e.g., just twice the value of `fisherz`.

### Author(s)

Thomas W. Yee

### See Also

`Links`, `binom2.rho`, `fisherz`.

### Examples

    theta <- seq(-0.99, 0.99, by = 0.01)
    y <- rhobit(theta)
    ## Not run:
    plot(theta, y, type = "l", las = 1, ylab = "", main = "rhobit(theta)")
    abline(v = 0, h = 0, lty = 2)

    ## End(Not run)

    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

[Package VGAM version 1.0-3 Index]