VGAM (version 1.0-1)

logoff: Log link function with an offset

Description

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

Usage

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

Arguments

theta

Numeric or character. See below for further details.

offset

Offset value. See Links.

inverse, deriv, short, tag

Details at Links.

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.

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.

References

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

See Also

Links, loge.

Examples

logoff(seq(-0.2, 0.5, by = 0.1))
logoff(seq(-0.2, 0.5, by = 0.1), offset = 0.5)
   log(seq(-0.2, 0.5, by = 0.1) + 0.5)