VGAM (version 1.1-11)

logofflink: Log Link Function with an Offset

Description

Computes the log transformation with an offset, including its inverse and the first two derivatives.

Usage

logofflink(theta, offset = 0, inverse = FALSE, deriv = 0,
           short = TRUE, tag = FALSE)
log1plink(theta, offset = 0, inverse = FALSE, deriv = 0,
          short = TRUE, tag = FALSE)

Value

For deriv = 0, the log of theta+offset, i.e.,

log(theta+offset) when inverse = FALSE, and if inverse = TRUE then

exp(theta)-offset.

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.

Here, all logarithms are natural logarithms, i.e., to base e.

Arguments

theta

Numeric or character. See below for further details.

offset

Offset value. See Links. For log1plink this argument should not be used because the offset is implicitly unity .

inverse, deriv, short, tag

Details at Links.

Author

Thomas W. Yee

Details

The log-offset link function is very commonly used for parameters that are greater than a certain value. In particular, it is defined by log(theta + offset) where offset is the offset value. For example, if offset = 0.5 then the value of theta is restricted to be greater than $-0.5$.

Numerical values of theta close to -offset or out of range result in Inf, -Inf, NA or NaN.

The offset is implicitly 1 in log1plink. It is equivalent to logofflink(offset = 1) but is more accurate if abs(theta) is tiny. It may be used for lrho in extbetabinomial provided an offset log(size - 1) for ${\eta }_2$ is included.

References

McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models, 2nd ed. London: Chapman & Hall.

See Also

Links, loglink, extbetabinomial.

Examples

if (FALSE) {
logofflink(seq(-0.2, 0.5, by = 0.1))
logofflink(seq(-0.2, 0.5, by = 0.1), offset = 0.5)
       log(seq(-0.2, 0.5, by = 0.1) + 0.5) }