Transformation from the Link Scale to the Observation Scale

The function transforms a variable from the link scale to the observation scale: probability or count.

invlink(x, type = c("cloglog", "log", "logit"))

Arguments

x

A vector of real numbers.

type

A character string. Legal values are “cloglog”, “log” and “logit”.

Value

\(anti-logit(x) = exp(x) / (1 + exp(x))\)
\(anti-cloglog(x) = 1 - exp(-exp(x))\)

See also

link

Examples

  x <- seq(-5, 5, length = 100)
  plot(x, invlink(x, type = "logit"),
       type = "l", lwd = 2, ylab = "Probability")
  lines(x, invlink(x, type = "cloglog"), lty = 2, lwd = 2)
  grid(col = "black")
  legend(-5, 1, legend = c("alogit(x)", "acloglog(x)"),
         lty = c(1, 2), bg = "white")