# multinomial logistic regression

library(car)
data(Womenlf)
attach(Womenlf)

# make ordered factor
participation <- ordered(partic,
levels=c('not.work', 'parttime', 'fulltime'))

## Fit model

library(nnet)
mod.multinom <- multinom(participation ~ hincome + children)
## # weights:  12 (6 variable)
## initial  value 288.935032
## iter  10 value 211.454772
## final  value 211.440963
## converged
summary(mod.multinom, Wald=TRUE)
## Call:
## multinom(formula = participation ~ hincome + children)
##
## Coefficients:
##          (Intercept)      hincome childrenpresent
## parttime   -1.432321  0.006893838      0.02145558
## fulltime    1.982842 -0.097232073     -2.55860537
##
## Std. Errors:
##          (Intercept)    hincome childrenpresent
## parttime   0.5924627 0.02345484       0.4690352
## fulltime   0.4841789 0.02809599       0.3621999
##
## Value/SE (Wald statistics):
##          (Intercept)    hincome childrenpresent
## parttime   -2.417573  0.2939197      0.04574407
## fulltime    4.095266 -3.4607098     -7.06407045
##
## Residual Deviance: 422.8819
## AIC: 434.8819
Anova(mod.multinom)
## Analysis of Deviance Table (Type II tests)
##
## Response: participation
##          LR Chisq Df Pr(>Chisq)
## hincome    15.153  2  0.0005123 ***
## children   63.559  2  1.579e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Plot fitted values

predictors <- expand.grid(hincome=1:45, children=c('absent', 'present'))
p.fit <- predict(mod.multinom, predictors, type='probs')

Hinc <- 1:max(hincome)
plot(range(hincome), c(0,1),
type='n', xlab="Husband's Income", ylab='Fitted Probability',
main="Children absent")
lines(Hinc, p.fit[Hinc, 'not.work'], lty=1, lwd=3, col="black")
lines(Hinc, p.fit[Hinc, 'parttime'], lty=2, lwd=3, col="blue")
lines(Hinc, p.fit[Hinc, 'fulltime'], lty=3, lwd=3, col="red")

legend(5, 0.97, lty=1:3, lwd=3, col=c("black", "blue", "red"),
legend=c('not working', 'part-time', 'full-time'))  

plot(range(hincome), c(0,1),
type='n', xlab="Husband's Income", ylab='Fitted Probability',
main="Children present")
lines(Hinc, p.fit[46:90, 'not.work'], lty=1, lwd=3, col="black")
lines(Hinc, p.fit[46:90, 'parttime'], lty=2, lwd=3, col="blue")
lines(Hinc, p.fit[46:90, 'fulltime'], lty=3, lwd=3, col="red")

# a more general way to make the plot
op <- par(mfrow=c(1,2))
Hinc <- 1:max(hincome)
for ( kids in c("absent", "present") ) {
data <- subset(data.frame(predictors, p.fit), children==kids)
plot( range(hincome), c(0,1), type="n",
xlab="Husband's Income", ylab='Fitted Probability',
main = paste("Children", kids))
lines(Hinc, data[, 'not.work'], lwd=3, col="black", lty=1)
lines(Hinc, data[, 'parttime'], lwd=3, col="blue",  lty=2)
lines(Hinc, data[, 'fulltime'], lwd=3, col="red",   lty=3)
if (kids=="absent") {
legend(5, 0.97, lty=1:3, lwd=3, col=c("black", "blue", "red"),
legend=c('not working', 'part-time', 'full-time'))
}
}

par(op)

detach(Womenlf)