VGAM (version 1.0-4)

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. 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.

`Links`, `logit`, `cloglog`, `cauchit`.

Examples

Run this code
```# 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)
# }
```

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