## Description

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

## Usage

 ```1 2``` ```rhobitlink(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 `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`.

## 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 `rhobitlink` is very similar to `fisherzlink`, e.g., just twice the value of `fisherzlink`.

## Author(s)

Thomas W. Yee

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```theta <- seq(-0.99, 0.99, by = 0.01) y <- rhobitlink(theta) ## Not run: plot(theta, y, type = "l", las = 1, ylab = "", main = "rhobitlink(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)) rhobitlink(x) # Has NAs rhobitlink(x, bminvalue = -1 + .Machine\$double.eps, bmaxvalue = 1 - .Machine\$double.eps) # Has no NAs ```

### Example output ```Loading required package: stats4