## Description

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

## Usage

 ```1 2``` ```powerlink(theta, power = 1, inverse = FALSE, deriv = 0, short = TRUE, tag = FALSE) ```

## Arguments

 `theta` Numeric or character. See below for further details. `power` This denotes the power or exponent. `inverse, deriv, short, tag` Details at `Links`.

## Details

The power link function raises a parameter by a certain value of `power`. Care is needed because it is very easy to get numerical problems, e.g., if `power=0.5` and `theta` is negative.

## Value

For `powerlink` with `deriv = 0`, then `theta` raised to the power of `power`. And if `inverse = TRUE` then `theta` raised to the power of `1/power`.

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.

## Note

Numerical problems may occur for certain combinations of `theta` and `power`. Consequently this link function should be used with caution.

## Author(s)

Thomas W. Yee

`Links`, `loglink`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```powerlink("a", power = 2, short = FALSE, tag = TRUE) powerlink(x <- 1:5) powerlink(x, power = 2) max(abs(powerlink(powerlink(x, power = 2), power = 2, inverse = TRUE) - x)) # Should be 0 powerlink(x <- (-5):5, power = 0.5) # Has NAs # 1/2 = 0.5 pdata <- data.frame(y = rbeta(n = 1000, shape1 = 2^2, shape2 = 3^2)) fit <- vglm(y ~ 1, betaR(lshape1 = powerlink(power = 0.5), i1 = 3, lshape2 = powerlink(power = 0.5), i2 = 7), data = pdata) t(coef(fit, matrix = TRUE)) Coef(fit) # Useful for intercept-only models vcov(fit, untransform = TRUE) ```

### Example output

```Loading required package: stats4
 1 2 3 4 5
  1  4  9 16 25
 0
      NaN      NaN      NaN      NaN      NaN 0.000000 1.000000 1.414214
 1.732051 2.000000 2.236068
(Intercept)