% \VignetteIndexEntry{Travel Mode - Multinomial Logit Model}
% \VignetteDepends{mlogit, Ecdat}
%\VignetteEngine{knitr::knitr}
%\VignetteEncoding{UTF-8}
\documentclass[a4paper]{article}

\title{Travel Mode - Multinomial Logit Model}

\begin{document}

\maketitle


<<echo=FALSE,eval=FALSE>>=
options(width=80)
@

For multinomial models that include category--specific as well as global effects the
function "mlogit" from the library "mlogit" can be used.

<<eval=FALSE>>=
library(mlogit)
@

The  "Travel Mode"--data are stored in the "Edcat"--package and can be loaded by the following
command.

<<eval=FALSE>>=
data(ModeChoice, package="Ecdat")
@

For the use of the function "mlogit"  an appropriate data set has to be built. This is done by  use of
the function "mlogit.data". 

<<eval=FALSE>>=
travel.long <- mlogit.data(ModeChoice, choice="mode", shape="long", alt.levels=
c("air","train","bus","car"))
@

Now  the model can be fitted. In the formula first the category--specific effects and then, 
separated by "|", the global effects are specified.

<<eval=FALSE>>=
travel.kat.id <- mlogit(mode ~ invt + gc|hinc, data=travel.long)
summary(travel.kat.id)
@

Now the same model is fitted with the package "VGAM".

<<eval=FALSE>>=
library(VGAM)
@

At first the data need to be prepared adequately to be ready for use with the function "vglm".

<<eval=FALSE>>=
travelmode <- matrix(ModeChoice$mode, byrow = T, ncol = 4)
colnames(travelmode) <- c("air","train","bus","car")
travelhinc <- matrix(ModeChoice$hinc, byrow = T, ncol = 4)
travelhinc <- travelhinc[,1]
travelinvt <- matrix(ModeChoice$invt, byrow = T, ncol = 4)
colnames(travelinvt) <- c("invtair","invttrain","invtbus","invtcar")
travelgc <- matrix(ModeChoice$gc, byrow = T, ncol = 4)
colnames(travelgc) <- c("gcair","gctrain","gcbus","gccar")

travelinvt <- sweep(travelinvt[,-1], 1, travelinvt[,1])
travelgc <- sweep(travelgc[,-1], 1, travelgc[,1])


Invt <- travelinvt[,1]
Gc <- travelgc[,1]

traveldat <- cbind(travelhinc, travelinvt, Invt, travelgc, Gc)
traveldat <- as.data.frame(traveldat)
@

Now the model can be fitted.

<<eval=FALSE>>=
fit <- vglm(travelmode ~ Invt + Gc + travelhinc,
            multinomial(parallel = FALSE ~ travelhinc, refLevel = 1),
            xij = list(Invt ~ invttrain + invtbus + invtcar,
                       Gc ~ gctrain + gcbus + gccar),
            form2 = ~ Invt + invttrain + invtbus + invtcar +
                      Gc + gctrain + gcbus + gccar + travelhinc,
            data = traveldat, trace = TRUE)

summary(fit)
summary(travel.kat.id)
@

At last we compare the coefficients of the two fitted models.

<<eval=FALSE>>=
summary(travel.kat.id)$CoefTable
summary(fit)@coef3
@

<<echo=FALSE,results='hide',eval=FALSE>>=
detach(package:VGAM)
detach(package:mlogit)
@

\end{document}