multilogit
Multi-logit Link Function
Computes the multilogit transformation, including its inverse and the first two derivatives.
- Keywords
- models, regression, math
Usage
multilogit(theta, refLevel = "(Last)", M = NULL, whitespace = FALSE,
bvalue = NULL, inverse = FALSE, deriv = 0, all.derivs = FALSE,
short = TRUE, tag = FALSE)Arguments
- theta
Numeric or character. See below for further details.
- refLevel, M, whitespace
See
multinomial.- bvalue
See
Links.- all.derivs
Logical. This is currently experimental only.
- inverse, deriv, short, tag
Details at
Links.
Details
The multilogit() link function is a generalization of the
logit 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.
When its inverse function is computed it returns values which
are positive and add to unity.
Value
For multilogit 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.
Note
Numerical instability may occur when theta is
close to 1 or 0 (for multilogit).
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.
References
McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models, 2nd ed. London: Chapman & Hall.
See Also
Links,
multinomial,
logit,
normal.vcm,
CommonVGAMffArguments.
Examples
# NOT RUN {
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)
multilogit(fitted(fit))
multilogit(fitted(fit)) - predict(fit) # Should be all 0s
multilogit(predict(fit), inverse = TRUE) # rowSums() add to unity
multilogit(predict(fit), inverse = TRUE, refLevel = 1) # For illustration only
multilogit(predict(fit), inverse = TRUE) - fitted(fit) # Should be all 0s
multilogit(fitted(fit), deriv = 1)
multilogit(fitted(fit), deriv = 2)
# }