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

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 $\log (θ)$ whereas negloglink computes $- \log (θ) = \log (1 / θ)$ .

The function logneglink computes $\log (- θ)$ , 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.

Examples

Run this code

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))

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