loge: Log link function, and variants

Description

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

Usage

loge(theta, bvalue = NULL, inverse = FALSE, deriv = 0,
     short = TRUE, tag = FALSE)
negloge(theta, bvalue = NULL, inverse = FALSE, deriv = 0,
        short = TRUE, tag = FALSE)
logneg(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 loge. 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 loge computes $\log(\theta)$ whereas negloge computes $-\log(\theta)=\log(1/\theta)$.

The function logneg 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.

Examples

Run this code

loge(seq(-0.2, 0.5, by = 0.1))
 loge(seq(-0.2, 0.5, by = 0.1), bvalue = .Machine$double.xmin)
negloge(seq(-0.2, 0.5, by = 0.1))
negloge(seq(-0.2, 0.5, by = 0.1), bvalue = .Machine$double.xmin)
logneg(seq(-0.5, -0.2, by = 0.1))

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