Log Link Function, and Variants

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

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.

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.

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.

References

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

Author

Thomas W. Yee

Note

This function was called loge to avoid conflict with the log function. Numerical instability may occur when theta is close to 0 unless bvalue is used.

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$double.xmin)
#> [1] -708.3964185 -708.3964185 -708.3964185   -2.3025851   -1.6094379
#> [6]   -1.2039728   -0.9162907   -0.6931472
negloglink(seq(-0.2, 0.5, by = 0.1))
#> [1]       NaN       NaN       Inf 2.3025851 1.6094379 1.2039728 0.9162907
#> [8] 0.6931472
negloglink(seq(-0.2, 0.5, by = 0.1), bvalue = .Machine$double.xmin)  # \dontrun{}
#> [1] 708.3964185 708.3964185 708.3964185   2.3025851   1.6094379   1.2039728
#> [7]   0.9162907   0.6931472
logneglink(seq(-0.5, -0.2, by = 0.1))
#> [1] -0.6931472 -0.9162907 -1.2039728 -1.6094379