Arcsine Link Function

Computes the arcsine link, including its inverse and the first few derivatives.

Usage

asinlink(theta, bvalue = NULL, inverse = FALSE,
   deriv = 0, short = TRUE, tag = FALSE, c10 = c(4, -pi))

Arguments

theta

Numeric or character. See below for further details.

bvalue

See Links.

inverse, deriv, short, tag

Details at Links.

c10

Similar to sqrtlink. The default is intended to match lcalogitlink for binomialff at binomial probabilities (theta) equal to 0.5.

Details

Function alogitlink gives some motivation for this link. However, the problem with this link is that it is bounded by default between (-pi, pi) so that it can be unsuitable for regression. This link is a scaled and centred CDF of the arcsine distribution. The centring is chosen so that asinlink(0.5) is 0, and the scaling is chosen so that asinlink(0.5, deriv = 1) and logitlink(0.5, deriv = 1) are equal (the value 4 actually), hence this link will operate similar to the logitlink when close to 0.5.

Value

Similar to logitlink but using different formulas.

Author

Thomas W. Yee

Warning

It is possible that the scaling might change in the future.

Examples

p <- seq(0.01, 0.99, length= 10)
asinlink(p)
#>  [1] -2.7409230 -1.7334784 -1.1514533 -0.6655492 -0.2182104  0.2182104
#>  [7]  0.6655492  1.1514533  1.7334784  2.7409230
max(abs(asinlink(asinlink(p), inv = TRUE) - p))  # 0?
#> [1] 1.110223e-16

if (FALSE) { # \dontrun{
par(mfrow = c(2, 2), lwd = (mylwd <- 2))
y <- seq(-4, 4, length = 100)
p <- seq(0.01, 0.99, by = 0.01)

for (d in 0:1) {
  matplot(p, cbind(logitlink(p, deriv = d), probitlink(p, deriv = d)),
          type = "n", col = "blue", ylab = "transformation",
          log = ifelse(d == 1, "y", ""),
          las = 1, main = if (d == 0) "Some probability link functions"
          else "First derivative")
  lines(p,   logitlink(p, deriv = d), col = "green")
  lines(p,  probitlink(p, deriv = d), col = "blue")
  lines(p, clogloglink(p, deriv = d), col = "tan")
  lines(p,    asinlink(p, deriv = d), col = "red3")
  if (d == 0) {
    abline(v = 0.5, h = 0, lty = "dashed")
    legend(0, 4.5, c("logitlink", "probitlink", "clogloglink",
           "asinlink"), lwd = mylwd,
           col = c("green", "blue", "tan", "red3"))
  } else
    abline(v = 0.5, lwd = 0.5, col = "gray")
}

for (d in 0) {
  matplot(y, cbind( logitlink(y, deriv = d, inverse = TRUE),
                   probitlink(y, deriv = d, inverse = TRUE)),
          type  = "n", col = "blue", xlab = "transformation", ylab = "p",
          main = if (d == 0) "Some inverse probability link functions"
          else "First derivative", las=1)
  lines(y,   logitlink(y, deriv = d, inverse = TRUE), col = "green")
  lines(y,  probitlink(y, deriv = d, inverse = TRUE), col = "blue")
  lines(y, clogloglink(y, deriv = d, inverse = TRUE), col = "tan")
  lines(y,    asinlink(y, deriv = d, inverse = TRUE), col = "red3")
  if (d == 0) {
      abline(h = 0.5, v = 0, lwd = 0.5, col = "gray")
      legend(-4, 1, c("logitlink", "probitlink", "clogloglink",
             "asinlink"), lwd = mylwd,
             col = c("green", "blue", "tan", "red3"))
  }
}
par(lwd = 1)
} # }