smtorres/GLMpack
Data and Code to Accompany Generalized Linear Models, 2nd Edition

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star: Data on California state data on educational policy and...

star: Data on California state data on educational policy and...
In smtorres/GLMpack: Data and Code to Accompany Generalized Linear Models, 2nd Edition

Description Usage Format Examples

Description

Data for the STAR program example used in chapter 6

Usage

1
data(star)

Format

A data frame with 303 rows and 16 variables:

LOWINC

Proportion of low-income students

PERASIAN

Proportions of Asian students

PERBLACK

Proportions of African-American students

PERHISP

Proportions of Hispanic students

PERMINTE

Percentage of minority teachers

AVYRSEXP

Mean teacher experience in years

AVSAL

Median teacher salary, including benefits, in thousands of dollars

PERSPEN

Per-pupil expenditures in thousands of dollars

PTRATIO

Pupil/teacher ratio in the classroom

PCTAF

Percentage of students taking college credit courses

PCTCHRT

Percentage of schools in the district that are charter schools

PCTYRRND

Percent of schools in the district operating year-round programs

READTOT

Total number of students taking the reading exam in the 9th grade

PR50RD

Proportion of students scoring over the reading median in the 9th grade

MATHTOT

Total number of students taking the math exam in the 9th grade

PR50M

Proportion of students scoring over the math median in the 9th grade

...

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data(star)
attach(star)

## MATH MODEL
star.logit.fit <- glm(cbind(PR50M,MATHTOT-PR50M) ~ LOWINC + PERASIAN + PERBLACK + PERHISP +
                  PERMINTE * AVYRSEXP * AVSAL + PERSPEN * PTRATIO * PCTAF +
                  PCTCHRT + PCTYRRND, family=binomial(link=logit),data=star)

## READING MODEL
star.logit.fit2 <- glm(cbind(PR50RD,READTOT-PR50RD) ~ LOWINC + PERASIAN + PERBLACK + PERHISP +
                   PERMINTE * AVYRSEXP * AVSAL + PERSPEN * PTRATIO * PCTAF +
                   PCTCHRT + PCTYRRND, family=binomial(link=logit),data=star)

## Table 6.4
star.summ.mat <- round(summary(star.logit.fit)$coef, 4)
data.frame(cbind(star.summ.mat[,1], star.summ.mat[,2], "[", round(confint(star.logit.fit)[,1],4),
      " ~", round(confint(star.logit.fit)[,2],4), "]"))

## Table 6.5
mean.vector <- apply(star,2,mean)
diff.vector <- c(1,mean.vector[1:12],mean.vector[5]*mean.vector[6],mean.vector[5]*mean.vector[7],
                 mean.vector[6]*mean.vector[7],mean.vector[8]*mean.vector[9],
                 mean.vector[8]*mean.vector[10],mean.vector[9]*mean.vector[10],
                 mean.vector[5]*mean.vector[6]*mean.vector[7],
                 mean.vector[8]*mean.vector[9]*mean.vector[10])
names(diff.vector) <- names(summary(star.logit.fit2)$coef[,1])
# PERMINTE FIRST DIFFERENCE ACROSS IQR
logit <- function(vec){return(exp(vec)/(1+exp(vec)))}
logit(c(diff.vector[1:5],6.329,diff.vector[7:13],6.329*mean.vector[6],6.329*mean.vector[7],
        diff.vector[16:19],6.329*mean.vector[6]*mean.vector[7],diff.vector[21])
      %*%summary.glm(star.logit.fit)$coef[,1]) -
logit(c(diff.vector[1:5],19.180,diff.vector[7:13],19.180*mean.vector[6],19.180*mean.vector[7],
          diff.vector[16:19],19.180*mean.vector[6]*mean.vector[7],diff.vector[21])
        %*%summary.glm(star.logit.fit)$coef[,1])
# First quartile information
q1.diff.mat <- q2.diff.mat <- q3.diff.mat <- q4.diff.mat <-
  matrix(rep(diff.vector,length(diff.vector)),
                      nrow=length(diff.vector), ncol=length(diff.vector),
                      dimnames=list(names(diff.vector),names(diff.vector)))
diag(q1.diff.mat)[2:13] <- apply(star,2,summary)[2,1:12]
q1.diff.mat[14,6] <- q1.diff.mat[6,6]*q1.diff.mat[7,6]
q1.diff.mat[15,6] <- q1.diff.mat[6,6]*q1.diff.mat[8,6]
q1.diff.mat[20,6] <- q1.diff.mat[6,6]*q1.diff.mat[7,6]*q1.diff.mat[8,6]
q1.diff.mat[14,7] <- q1.diff.mat[7,7]*q1.diff.mat[6,7]
q1.diff.mat[16,7] <- q1.diff.mat[7,7]*q1.diff.mat[8,7]
q1.diff.mat[20,7] <- q1.diff.mat[6,7]*q1.diff.mat[7,7]*q1.diff.mat[8,7]
q1.diff.mat[15,8] <- q1.diff.mat[8,8]*q1.diff.mat[6,8]
q1.diff.mat[16,8] <- q1.diff.mat[8,8]*q1.diff.mat[7,8]
q1.diff.mat[20,8] <- q1.diff.mat[6,8]*q1.diff.mat[7,8]*q1.diff.mat[8,8]
q1.diff.mat[17,9] <- q1.diff.mat[9,9]*q1.diff.mat[10,9]
q1.diff.mat[18,9] <- q1.diff.mat[9,9]*q1.diff.mat[11,9]
q1.diff.mat[21,9] <- q1.diff.mat[9,9]*q1.diff.mat[10,9]*q1.diff.mat[11,9]
q1.diff.mat[17,10] <- q1.diff.mat[10,10]*q1.diff.mat[9,10]
q1.diff.mat[19,10] <- q1.diff.mat[10,10]*q1.diff.mat[11,10]
q1.diff.mat[21,10] <- q1.diff.mat[9,10]*q1.diff.mat[10,10]*q1.diff.mat[11,10]
q1.diff.mat[18,11] <- q1.diff.mat[11,11]*q1.diff.mat[9,11]
q1.diff.mat[19,11] <- q1.diff.mat[11,11]*q1.diff.mat[10,11]
q1.diff.mat[21,11] <- q1.diff.mat[9,11]*q1.diff.mat[10,11]*q1.diff.mat[11,11]
# Third quartile
diag(q2.diff.mat)[2:13] <- apply(star,2,summary)[5,1:12]
q2.diff.mat[14,6] <- q2.diff.mat[6,6]*q2.diff.mat[7,6]
q2.diff.mat[15,6] <- q2.diff.mat[6,6]*q2.diff.mat[8,6]
q2.diff.mat[20,6] <- q2.diff.mat[6,6]*q2.diff.mat[7,6]*q2.diff.mat[8,6]
q2.diff.mat[14,7] <- q2.diff.mat[7,7]*q2.diff.mat[6,7]
q2.diff.mat[16,7] <- q2.diff.mat[7,7]*q2.diff.mat[8,7]
q2.diff.mat[20,7] <- q2.diff.mat[6,7]*q2.diff.mat[7,7]*q2.diff.mat[8,7]
q2.diff.mat[15,8] <- q2.diff.mat[8,8]*q2.diff.mat[6,8]
q2.diff.mat[16,8] <- q2.diff.mat[8,8]*q2.diff.mat[7,8]
q2.diff.mat[20,8] <- q2.diff.mat[6,8]*q2.diff.mat[7,8]*q2.diff.mat[8,8]
q2.diff.mat[17,9] <- q2.diff.mat[9,9]*q2.diff.mat[10,9]
q2.diff.mat[18,9] <- q2.diff.mat[9,9]*q2.diff.mat[11,9]
q2.diff.mat[21,9] <- q2.diff.mat[9,9]*q2.diff.mat[10,9]*q2.diff.mat[11,9]
q2.diff.mat[17,10] <- q2.diff.mat[10,10]*q2.diff.mat[9,10]
q2.diff.mat[19,10] <- q2.diff.mat[10,10]*q2.diff.mat[11,10]
q2.diff.mat[21,10] <- q2.diff.mat[9,10]*q2.diff.mat[10,10]*q2.diff.mat[11,10]
q2.diff.mat[18,11] <- q2.diff.mat[11,11]*q2.diff.mat[9,11]
q2.diff.mat[19,11] <- q2.diff.mat[11,11]*q2.diff.mat[10,11]
q2.diff.mat[21,11] <- q2.diff.mat[9,11]*q2.diff.mat[10,11]*q2.diff.mat[11,11]
# Minimum
diag(q3.diff.mat)[2:13] <- apply(star,2,summary)[1,1:12]
q3.diff.mat[14,6] <- q3.diff.mat[6,6]*q3.diff.mat[7,6]
q3.diff.mat[15,6] <- q3.diff.mat[6,6]*q3.diff.mat[8,6]
q3.diff.mat[20,6] <- q3.diff.mat[6,6]*q3.diff.mat[7,6]*q3.diff.mat[8,6]
q3.diff.mat[14,7] <- q3.diff.mat[7,7]*q3.diff.mat[6,7]
q3.diff.mat[16,7] <- q3.diff.mat[7,7]*q3.diff.mat[8,7]
q3.diff.mat[20,7] <- q3.diff.mat[6,7]*q3.diff.mat[7,7]*q3.diff.mat[8,7]
q3.diff.mat[15,8] <- q3.diff.mat[8,8]*q3.diff.mat[6,8]
q3.diff.mat[16,8] <- q3.diff.mat[8,8]*q3.diff.mat[7,8]
q3.diff.mat[20,8] <- q3.diff.mat[6,8]*q3.diff.mat[7,8]*q3.diff.mat[8,8]
q3.diff.mat[17,9] <- q3.diff.mat[9,9]*q3.diff.mat[10,9]
q3.diff.mat[18,9] <- q3.diff.mat[9,9]*q3.diff.mat[11,9]
q3.diff.mat[21,9] <- q3.diff.mat[9,9]*q3.diff.mat[10,9]*q3.diff.mat[11,9]
q3.diff.mat[17,10] <- q3.diff.mat[10,10]*q3.diff.mat[9,10]
q3.diff.mat[19,10] <- q3.diff.mat[10,10]*q3.diff.mat[11,10]
q3.diff.mat[21,10] <- q3.diff.mat[9,10]*q3.diff.mat[10,10]*q3.diff.mat[11,10]
q3.diff.mat[18,11] <- q3.diff.mat[11,11]*q3.diff.mat[9,11]
q3.diff.mat[19,11] <- q3.diff.mat[11,11]*q3.diff.mat[10,11]
q3.diff.mat[21,11] <- q3.diff.mat[9,11]*q3.diff.mat[10,11]*q3.diff.mat[11,11]
diag(q4.diff.mat)[2:13] <- apply(star,2,summary)[6,1:12]
q4.diff.mat[14,6] <- q4.diff.mat[6,6]*q4.diff.mat[7,6]
q4.diff.mat[15,6] <- q4.diff.mat[6,6]*q4.diff.mat[8,6]
q4.diff.mat[20,6] <- q4.diff.mat[6,6]*q4.diff.mat[7,6]*q2.diff.mat[8,6]
q4.diff.mat[14,7] <- q4.diff.mat[7,7]*q4.diff.mat[6,7]
q4.diff.mat[16,7] <- q4.diff.mat[7,7]*q4.diff.mat[8,7]
q4.diff.mat[20,7] <- q4.diff.mat[6,7]*q4.diff.mat[7,7]*q4.diff.mat[8,7]
q4.diff.mat[15,8] <- q4.diff.mat[8,8]*q4.diff.mat[6,8]
q4.diff.mat[16,8] <- q4.diff.mat[8,8]*q4.diff.mat[7,8]
q4.diff.mat[20,8] <- q4.diff.mat[6,8]*q4.diff.mat[7,8]*q4.diff.mat[8,8]
q4.diff.mat[17,9] <- q4.diff.mat[9,9]*q4.diff.mat[10,9]
q4.diff.mat[18,9] <- q4.diff.mat[9,9]*q4.diff.mat[11,9]
q4.diff.mat[21,9] <- q4.diff.mat[9,9]*q4.diff.mat[10,9]*q4.diff.mat[11,9]
q4.diff.mat[17,10] <- q4.diff.mat[10,10]*q4.diff.mat[9,10]
q4.diff.mat[19,10] <- q4.diff.mat[10,10]*q4.diff.mat[11,10]
q4.diff.mat[21,10] <- q4.diff.mat[9,10]*q4.diff.mat[10,10]*q4.diff.mat[11,10]
q4.diff.mat[18,11] <- q4.diff.mat[11,11]*q4.diff.mat[9,11]
q4.diff.mat[19,11] <- q4.diff.mat[11,11]*q4.diff.mat[10,11]
q4.diff.mat[21,11] <- q4.diff.mat[9,11]*q4.diff.mat[10,11]*q4.diff.mat[11,11]
first_diffs <- NULL
for (i in 2:13){
        temp1 <- logit(q2.diff.mat[,i]%*%summary.glm(star.logit.fit)$coef[,1]) -
                        logit(q1.diff.mat[,i]%*%summary.glm(star.logit.fit)$coef[,1])
        temp2 <- logit(q4.diff.mat[,i]%*%summary.glm(star.logit.fit)$coef[,1]) -
          logit(q3.diff.mat[,i]%*%summary.glm(star.logit.fit)$coef[,1])
        first_diffs <- rbind(first_diffs, c(temp1,temp2))
}
first_diffs <- round(first_diffs,4)
diffs_mat <- cbind(diag(q1.diff.mat)[2:13], diag(q2.diff.mat)[2:13],
                   first_diffs[,1],
                   diag(q3.diff.mat)[2:13], diag(q4.diff.mat)[2:13],
                   first_diffs[,2])
colnames(diffs_mat) <- c("1st quartile", "3rd quartile", "Interquartile 1st diff",
                         "Min", "Max", "Full range 1st diff")
diffs_mat

star.mu <- predict.glm(star.logit.fit,type="response")
star.y <- PR50M/MATHTOT
star.n <- length(star.y)
PR50M.adj <- PR50M
for (i in 1:length(PR50M.adj))  {
  if (PR50M.adj[i] > mean(PR50M)) PR50M.adj[i] <- PR50M.adj[i] - 0.5
  if (PR50M.adj[i] < mean(PR50M)) PR50M.adj[i] <- PR50M.adj[i] + 0.5
}
par(mfrow=c(1,3), mar=c(6,3,6,2),oma=c(4,1,4,1))
plot(star.mu,star.y,xlab="",ylab="", yaxt='n', xaxt="n", pch="+")
axis(1, tck=0.02, cex.axis=0.9, mgp=c(0.3, 0.3, 0), lty=1, lwd=0, lwd.ticks = 1)
axis(2, tck=0.02, cex.axis=0.9, mgp=c(0.3, 0.3, 0), lty=1, lwd=0, lwd.ticks = 1, las=2)
title(xlab = "Fitted values", ylab="Observed values",
      line = 1.7, cex.lab=1.3)
title(main="Model Fit Plot",
      line = 1, cex.main=1.7, font.main=1)
abline(lm(star.y~star.mu)$coefficients, lwd=2)
plot(fitted(star.logit.fit),resid(star.logit.fit,type="pearson"),xlab="",ylab="",
     yaxt='n', xaxt="n", pch="+")
axis(1, tck=0.02, cex.axis=0.9, mgp=c(0.3, 0.3, 0), lty=1, lwd=0, lwd.ticks = 1)
axis(2, tck=0.02, cex.axis=0.9, mgp=c(0.3, 0.3, 0), lty=1, lwd=0, lwd.ticks = 1, las=2)
title(xlab = "Fitted values", ylab="Pearson Residuals",
      line = 1.7, cex.lab=1.3)
title(main="Residual Dependence Plot",
      line = 1, cex.main=1.7, font.main=1)
abline(0,0, lwd=2)
qqnorm(resid(star.logit.fit,type="deviance"),main="",xlab="",ylab="",
       yaxt='n', xaxt="n", pch="+")
axis(1, tck=0.02, cex.axis=0.9, mgp=c(0.3, 0.3, 0), lty=1, lwd=0, lwd.ticks = 1)
axis(2, tck=0.02, cex.axis=0.9, mgp=c(0.3, 0.3, 0), lty=1, lwd=0, lwd.ticks = 1, las=2)
title(xlab = "Quantiles of N(0,1)", ylab="Deviance Residual Quantiles",
      line = 1.7, cex.lab=1.3)
title(main="Normal-Quantile Plot",
      line = 1, cex.main=1.7, font.main=1)
abline(-0.3,3.5, lwd=2)
dev.off()

smtorres/GLMpack documentation built on July 21, 2019, 10:59 p.m.

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