logit {VGAM} | R Documentation |
Computes the logit transformation, including its inverse and the first two derivatives.
logit(theta, earg = list(), inverse = FALSE, deriv = 0, short = TRUE, tag = FALSE) elogit(theta, earg = list(min = 0, max = 1), 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 For |
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 logit link function is very 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 extended logit link function elogit
should be used
more generally for parameters that lie in the interval (A,B), say.
The formula is
log((theta-A)/(B-theta))
and the default values for A and B correspond to the ordinary
logit function.
Numerical values of theta
close to A or B or out of range
result in
Inf
, -Inf
, NA
or NaN
.
However these can be replaced by values bminvalue and
bmaxvalue first before computing the link function.
The arguments short
and tag
are used only if
theta
is character.
For logit
with deriv = 0
, the logit of theta
, i.e.,
log(theta/(1-theta))
when inverse = FALSE
,
and if inverse = TRUE
then
exp(theta)/(1+exp(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.
Here, all logarithms are natural logarithms, i.e., to base e.
Numerical instability may occur when theta
is
close to 1 or 0 (for logit
), or close to A or B for
elogit
.
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
logistic distribution (see logistic
).
Thomas W. Yee
McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models, 2nd ed. London: Chapman & Hall.
Links
,
probit
,
cloglog
,
cauchit
,
logistic1
,
loge
.
p = seq(0.01, 0.99, by = 0.01) logit(p) max(abs(logit(logit(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)) logit(p) # Has NAs logit(p, earg = list(bvalue = .Machine$double.eps)) # Has no NAs p = seq(0.9, 2.2, by = 0.1) elogit(p, earg = list(min = 1, max = 2, bminvalue = 1 + .Machine$double.eps, bmaxvalue = 2 - .Machine$double.eps)) # Has no NAs ## Not run: par(mfrow = c(2,2)) y = seq(-4, 4, length = 100) p = seq(0.01, 0.99, by = 0.01) for(d in 0:1) { matplot(p, cbind(logit(p, deriv = d), probit(p, deriv = d)), type = "n", col = "purple", ylab = "transformation", lwd = 2, las = 1, main = if (d == 0) "Some probability link functions" else "First derivative") lines(p, logit(p, deriv = d), lwd = 2, col = "limegreen") lines(p, probit(p, deriv = d), lwd = 2, col = "purple") lines(p, cloglog(p, deriv = d), lwd = 2, col = "chocolate") lines(p, cauchit(p, deriv = d), lwd = 2, col = "tan") if (d == 0) { abline(v = 0.5, h = 0, lty = "dashed") legend(0, 4.5, c("logit", "probit", "cloglog", "cauchit"), col = c("limegreen", "purple", "chocolate", "tan"), lwd = 2) } else abline(v = 0.5, lty = "dashed") } for(d in 0) { matplot(y, cbind(logit(y, deriv = d, inverse = TRUE), probit(y, deriv = d, inverse = TRUE)), type = "n", col = "purple", xlab = "transformation", ylab = "p", lwd = 2, las = 1, main = if (d == 0) "Some inverse probability link functions" else "First derivative") lines(y, logit(y, deriv = d, inverse = TRUE), lwd = 2, col = "limegreen") lines(y, probit(y, deriv = d, inverse = TRUE), lwd = 2, col = "purple") lines(y, cloglog(y, deriv = d, inverse = TRUE), lwd = 2, col = "chocolate") lines(y, cauchit(y, deriv = d, inverse = TRUE), lwd = 2, col = "tan") if (d == 0) { abline(h = 0.5, v = 0, lty = "dashed") legend(-4, 1, c("logit", "probit", "cloglog", "cauchit"), col = c("limegreen", "purple", "chocolate", "tan"), lwd = 2) } } p = seq(0.21, 0.59, by = 0.01) plot(p, elogit(p, earg = list(min = 0.2, max = 0.6)), lwd = 2, type = "l", col = "black", ylab = "transformation", xlim = c(0,1), las = 1, main = "elogit(p, earg = list(min = 0.2, max = 0.6)") ## End(Not run)