VGAM (version 0.9-4)

mlogit: Multi-logit Link Function

Description

Computes the mlogit transformation, including its inverse and the first two derivatives.

Usage

mlogit(theta, refLevel = "last", M = NULL, whitespace = FALSE,
       bvalue = NULL, inverse = FALSE, deriv = 0,
       short = TRUE, tag = FALSE)

Arguments

theta

Numeric or character. See below for further details.

refLevel, M, whitespace

See multinomial.

bvalue

See Links.

inverse, deriv, short, tag

Details at Links.

Value

• For mlogit with deriv = 0, the mlogit 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 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.

Details

The mlogit() 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.

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

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)

mlogit(fitted(fit))
mlogit(fitted(fit)) - predict(fit)  # Should be all 0s

mlogit(predict(fit), inverse = TRUE)  # rowSums() add to unity
mlogit(predict(fit), inverse = TRUE, refLevel = 1)  # For illustration only
mlogit(predict(fit), inverse = TRUE) - fitted(fit)  # Should be all 0s

mlogit(fitted(fit), deriv = 1)
mlogit(fitted(fit), deriv = 2)