VGAM (version 0.8-2)

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, earg = list(offset=0), inverse = FALSE, deriv = 0,
       short = TRUE, tag = FALSE)

Arguments

theta

Numeric or character. See below for further details.

earg

List. Extra argument for passing in additional information. The offset component of the list earg is the offset value. See Links for general information about earg

inverse

Logical. If TRUE the inverse function is computed.

deriv

Order of the derivative. Integer with value 0, 1 or 2.

short

Used for labelling the blurb slot of a vglmff-class object.

tag

Used for labelling the linear/additive predictor in the initialize slot of a vglmff-class object. Contains a little more information if TRUE.

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. The arguments short and tag are used only if theta is character.

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