powerlink {VGAM} | R Documentation

## Power Link Function

### 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`.

### 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

### See Also

`Links`, `loglink`.

### Examples

    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)

[Package VGAM version 1.1-1 Index]