VGAM (version 1.0-4)

logoff: Log Link Function with an Offset


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


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



Numeric or character. See below for further details.


Offset value. See Links.

inverse, deriv, short, tag

Details at Links.


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.


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.


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

See Also

Links, loge.


Run this code
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) 
# }

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