School Data

Description

School Data, from Charnes et al. (1981). The aim is to explain scores on 3 different tests, reading, mathematics and selfesteem from 70 school sites by means of 5 explanatory variables related to parents and teachers.

Format

A data frame with 70 observations on the following 8 variables.

education

Education level of mother as measured in terms of percentage of high school graduates among female parents

occupation

Highest occupation of a family member according to a pre-arranged rating scale

visit

Parental visits index representing the number of visits to the school site

counseling

Parent counseling index calculated from data on time spent with child on school-related topics such as reading together, etc.

teacher

Number of teachers at a given site

reading

Reading score as measured by the Metropolitan Achievement Test

mathematics

Mathematics score as measured by the Metropolitan Achievement Test

selfesteem

Coopersmith Self-Esteem Inventory, intended as a measure of self-esteem

Details

This dataset was shamelessly borrowed from the FRB package.

The relationships among these variables are unusual, a fact only revealed by plotting.

Source

A. Charnes, W.W. Cooper and E. Rhodes (1981). Evaluating Program and Managerial Efficiency: An Application of Data Envelopment Analysis to Program Follow Through. Management Science, 27, 668-697.

Examples

data(schooldata)
# initial screening
plot(schooldata)

# better plot
library(corrgram)
corrgram(schooldata, 
         lower.panel=panel.ellipse, 
         upper.panel=panel.pts)

#fit the MMreg model
school.mod <- lm(cbind(reading, mathematics, selfesteem) ~ 
		             education + occupation + visit + counseling + teacher, data=schooldata)

# shorthand: fit all others
school.mod <- lm(cbind(reading, mathematics, selfesteem) ~ ., data=schooldata)
car::Anova(school.mod)

# HE plots
heplot(school.mod, fill=TRUE, fill.alpha=0.1)
pairs(school.mod, fill=TRUE, fill.alpha=0.1)

# robust model, using robmlm()
school.rmod <- robmlm(cbind(reading, mathematics, selfesteem) ~ ., data=schooldata)
# note that counseling is now significant
car::Anova(school.rmod)

# Index plot of the weights
wts <- school.rmod$weights
notable <- which(wts < 0.8)
plot(wts, type = "h", col="gray", ylab = "Observation weight")
points(1:length(wts), wts, 
       pch=16,
       col = ifelse(wts < 0.8, "red", "black"))

text(notable, wts[notable],
     labels = notable,
     pos = 3,
     col = "red")



# compare classical HE plot with that based on the robust model
heplot(school.mod, cex=1.4, lty=1, fill=TRUE, fill.alpha=0.1)
heplot(school.rmod, 
       add=TRUE, 
       error.ellipse=TRUE, 
       lwd=c(2,2), lty=c(2,2), 
	     term.labels=FALSE, err.label="", 
	     fill=TRUE)