VGAM (version 0.9-1)

probit: Probit Link Function

Description

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

Usage

probit(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

• For deriv = 0, the probit of theta, i.e., qnorm(theta) when inverse = FALSE, and if inverse = TRUE then pnorm(theta).

  For deriv = 1, then the function returns d theta / d eta as a function of theta if inverse = FALSE, else if inverse = TRUE then it returns the reciprocal.

Details

The probit link function is commonly used for parameters that lie in the unit interval. Numerical values of theta close to 0 or 1 or out of range result in Inf, -Inf, NA or NaN.

References

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

See Also

Links, logit, cloglog, cauchit.

Examples

p <- seq(0.01, 0.99, by = 0.01)
probit(p)
max(abs(probit(probit(p), inverse = TRUE) - p)) # Should be 0

p <- c(seq(-0.02, 0.02, by = 0.01), seq(0.97, 1.02, by = 0.01))
probit(p) # Has NAs
probit(p, bvalue = .Machine$double.eps) # Has no NAs

p <- seq(0.01, 0.99, by = 0.01); par(lwd = (mylwd <- 2))
plot(p, logit(p), type = "l", col = "limegreen", ylab = "transformation",
     las = 1, main = "Some probability link functions")
lines(p,  probit(p), col = "purple")
lines(p, cloglog(p), col = "chocolate")
lines(p, cauchit(p), col = "tan")
abline(v = 0.5, h = 0, lty = "dashed")
legend(0.1, 4.0, c("logit", "probit", "cloglog", "cauchit"), 
       col = c("limegreen", "purple", "chocolate", "tan"), lwd = mylwd)
par(lwd = 1)