VGAM (version 1.1-8)

loglink: Log Link Function, and Variants

Description

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

Usage

loglink(theta, bvalue = NULL, inverse = FALSE, deriv = 0,
        short = TRUE, tag = FALSE)
negloglink(theta, bvalue = NULL, inverse = FALSE, deriv = 0,
           short = TRUE, tag = FALSE)
logneglink(theta, bvalue = NULL, inverse = FALSE, deriv = 0,
           short = TRUE, tag = FALSE)

Value

The following concerns loglink. For deriv = 0, the log of theta, i.e.,

log(theta) when inverse = FALSE, and if

inverse = TRUE then exp(theta). For deriv = 1, then the function returns

d

eta / d

theta as a function of

theta if inverse = FALSE, else if

inverse = TRUE then it returns the reciprocal.

Arguments

theta

Numeric or character. See below for further details.

bvalue

See Links.

inverse, deriv, short, tag

Details at Links.

Author

Thomas W. Yee

Details

The log link function is very commonly used for parameters that are positive. Here, all logarithms are natural logarithms, i.e., to base \(e\). Numerical values of theta close to 0 or out of range result in Inf, -Inf, NA or NaN.

The function loglink computes \(\log(\theta)\) whereas negloglink computes \(-\log(\theta)=\log(1/\theta)\).

The function logneglink computes \(\log(-\theta)\), hence is suitable for parameters that are negative, e.g., a trap-shy effect in posbernoulli.b.

References

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

See Also

Links, explink, logitlink, logclink, logloglink, log, logofflink, lambertW, posbernoulli.b.

Examples

if (FALSE)  loglink(seq(-0.2, 0.5, by = 0.1))
 loglink(seq(-0.2, 0.5, by = 0.1), bvalue = .Machine$double.xmin)
negloglink(seq(-0.2, 0.5, by = 0.1))
negloglink(seq(-0.2, 0.5, by = 0.1), bvalue = .Machine$double.xmin) 
logneglink(seq(-0.5, -0.2, by = 0.1))