asinlink: Arcsine Link Function

In VGAM: Vector Generalized Linear and Additive Models

Arcsine Link Function

Description

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.

Warning

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

Author(s)

Thomas W. Yee

See Also

logitlink, alogitlink, Links, probitlink, clogloglink, cauchitlink, binomialff, sloglink, hdeff.

Examples

p <- seq(0.01, 0.99, length= 10)
asinlink(p)
max(abs(asinlink(asinlink(p), inv = TRUE) - p))  # 0?

## Not run: 
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)

## End(Not run)

VGAM documentation built on Sept. 18, 2024, 9:09 a.m.