VGAM (version 1.0-6)

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 eta / d theta 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. It is the inverse CDF of the standard normal distribution. 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, Normal.

Examples

# NOT RUN {
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

# }
# NOT RUN {
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) 
# }