Showing Explained Variance in Multilevel Models

In this post I shows a quite intuitive manner of displaying explained variance of multilevel models using line charts.

For the best of my knowledge, there is no a default plot for displaying the effect of a factor on the deviance of multilevel models; so this is going to be a tentative for showing such a statistic in my ongoing dissertation.

The following values were obtained using multilevel models performed in R (thanks for nlme and lme4 packages). Basically, this chart shows the declining variance for each level when each independent parameter is included in the model. You can find the full script below the chart.

Explained Variance

Graph for explained variance

# camera 2002
df1<-data.frame(level3=c(0.5045094,0.1485807, 0.0494265),
level2=c(2.7814555,1.7936947, 1.6300276),
level1=c(3.7370482, 3.4816692, 3.4842407),
t=c(0,1, 2))
par(mfrow = c(2,2), mar = c(2,4, 2, 4))#Matrix
plot(df1$level1 ~ df1$t, type="l", lwd=4, col="red", xlab="", ylab="Variance",
main="Câmara 2002", cex.main = 1,
xlim=c(0,2), xaxt="n", ylim=c(0,4))
axis(1, c(0,1,2))#to remaque axis
lines(df1$level2 ~ df1$t, type="l", lwd=4, col="blue")
lines(df1$level3 ~ df1$t, type="l", lwd=4, col="purple")
text(locator(1), expression(sigma^2)) #need to click
text(locator(1), expression(tau[0][0])) # need to click to add the text
text(locator(1), expression(omega[0][0]))# need to click to add the text
# camera 2006
df3<-data.frame(level3=c(0.2562132,0.07523431, 0.04434483),
level2=c(1.7604626 ,1.2956322 , 1.08924671),
level1=c(2.2531888, 1.9952469 , 2.00465342),
t=c(0,1, 2))
plot(df3$level1 ~ df3$t, type="l", lwd=4, col="red", xlab="", ylab="Variance",
main="Câmara 2006", cex.main = 1,
xlim=c(0,2), xaxt="n", ylim=c(0,3))
axis(1, c(0,1,2))#to remaque axis
lines(df3$level2 ~ df3$t, type="l", lwd=4, col="blue")
lines(df3$level3 ~ df3$t, type="l", lwd=4, col="purple")
text(locator(1), expression(sigma^2)) # need to click to add the text
text(locator(1), expression(tau[0][0])) # need to click to add the text
text(locator(1), expression(omega[0][0])) # need to click to add the text
# senado 2002
df2<-data.frame(level2=c(74.1874,50.21794, 39.31336),
level1=c(165.1340, 163.19076, 156.08912),
t=c(0,1, 2))
plot(df2$level1 ~ df2$t, type="l", lwd=4, col="red", xlab="", ylab="Variance",
main="Senado 2002", cex.main = 1,
xlim=c(0,2), xaxt="n", ylim=c(30,170))
axis(1, c(0,1,2))
lines(df2$level2 ~ df2$t, type="l", lwd=4, col="blue")
text(locator(1), expression(sigma^2))# need to click to add the text
text(locator(1), expression(tau[0][0]))# need to click to add the text
# senado 2006
df4<-data.frame(level2=c(195.8233, 112.2718, 65.28095),
level1=c(292.0457, 270.1955, 250.65042),
t=c(0,1, 2))
plot(df4$level1 ~ df4$t, type="l", lwd=4, col="red", xlab="", ylab="Variance",
main="Senado 2006", cex.main = 1,
xlim=c(0,2), xaxt="n", ylim=c(50,300))
axis(1, c(0,1,2))
lines(df4$level2 ~ df4$t, type="l", lwd=4, col="blue")
text(locator(1), expression(sigma^2)) # need to click to add the text
text(locator(1), expression(tau[0][0])) # need to click to add the text

##End not run
comments powered by Disqus