# multinomial logistic regression
library(car)
data(Womenlf)
attach(Womenlf)
# make ordered factor
participation <- ordered(partic,
levels=c('not.work', 'parttime', 'fulltime'))
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)