Multi-logit Link Function
Computes the multilogit transformation, including its inverse and the first two derivatives.
multilogitlink(theta, refLevel = "(Last)", M = NULL, whitespace = FALSE,
bvalue = NULL, inverse = FALSE, deriv = 0, all.derivs = FALSE,
short = TRUE, tag = FALSE)theta |
Numeric or character. See below for further details. |
refLevel, M, whitespace |
See |
bvalue |
See |
all.derivs |
Logical. This is currently experimental only. |
inverse, deriv, short, tag |
Details at |
The multilogitlink() link function is a generalization of the
logitlink link to M levels/classes.
It forms the basis of the multinomial logit model.
It is sometimes called the multi-logit link
or the multinomial logit link;
some people use softmax too.
When its inverse function is computed it returns values which
are positive and add to unity.
For multilogitlink with deriv = 0, the multilogit of theta,
i.e.,
log(theta[, j]/theta[, M+1]) when inverse = FALSE,
and if inverse = TRUE then
exp(theta[, j])/(1+rowSums(exp(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.
Here, all logarithms are natural logarithms, i.e., to base e.
Numerical instability may occur when theta is
close to 1 or 0 (for multilogitlink).
One way of overcoming this is to use, e.g., bvalue.
Currently care.exp() is used to avoid NAs being
returned if the probability is too close to 1.
Thomas W. Yee
McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models, 2nd ed. London: Chapman & Hall.
pneumo <- transform(pneumo, let = log(exposure.time))
fit <- vglm(cbind(normal, mild, severe) ~ let,
multinomial, trace = TRUE, data = pneumo) # For illustration only!
fitted(fit)
predict(fit)
multilogitlink(fitted(fit))
multilogitlink(fitted(fit)) - predict(fit) # Should be all 0s
multilogitlink(predict(fit), inverse = TRUE) # rowSums() add to unity
multilogitlink(predict(fit), inverse = TRUE, refLevel = 1) # For illustration only
multilogitlink(predict(fit), inverse = TRUE) - fitted(fit) # Should be all 0s
multilogitlink(fitted(fit), deriv = 1)
multilogitlink(fitted(fit), deriv = 2)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.