VGAM (version 1.1-5)

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)

Arguments

theta

Numeric or character. See below for further details.

bvalue

See Links.

inverse, deriv, short, tag

Details at Links.

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.

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

# NOT RUN {
 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) 
# }
# NOT RUN {
logneglink(seq(-0.5, -0.2, by = 0.1))
# }