probit {VGAM} | R Documentation |
Computes the probit transformation, including its inverse and the first two derivatives.
probit(theta, earg = list(), inverse = FALSE, deriv = 0, short = TRUE, tag = FALSE)
theta |
Numeric or character. See below for further details. |
earg |
Optional list. Extra argument for passing in additional information.
Values of |
inverse |
Logical. If |
deriv |
Order of the derivative. Integer with value 0, 1 or 2. |
short |
Used for labelling the |
tag |
Used for labelling the linear/additive predictor in the
|
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
.
The arguments short
and tag
are used only if
theta
is character.
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.
Numerical instability may occur when theta
is close to 1 or 0.
One way of overcoming this is to use earg
.
In terms of the threshold approach with cumulative probabilities for
an ordinal response this link function corresponds to the univariate
normal distribution (see normal1
).
Thomas W. Yee
McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models, 2nd ed. London: Chapman & Hall.
Links
,
logit
,
cloglog
,
cauchit
.
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, earg=list(bvalue= .Machine$double.eps)) # Has no NAs ## Not run: p = seq(0.01, 0.99, by=0.01) plot(p, logit(p), type="l", col="limegreen", ylab="transformation", lwd=2, las=1, main="Some probability link functions") lines(p, probit(p), col="purple", lwd=2) lines(p, cloglog(p), col="chocolate", lwd=2) lines(p, cauchit(p), col="tan", lwd=2) 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=2) ## End(Not run)