VGAM (version 1.0-4)

## Description

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

## Usage

```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`.

## 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.

## 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.

`Links`, `loge`.

## Examples

Run this code
```# NOT RUN {
powerlink("a", power = 2, short = FALSE, tag = TRUE)
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)
# }
```

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