PublicSchools {sandwich} | R Documentation |
Per capita expenditure on public schools and per capita income by state in 1979.
data(PublicSchools)
A data frame containing 51 observations of 2 variables.
Table 14.1 in Greene (1993)
Cribari-Neto F. (2004), Asymptotic Inference Under Heteroskedasticity of Unknown Form, Computational Statistics & Data Analysis, 45, 215-233.
Greene W.H. (1993), Econometric Analysis, 2nd edition. Macmillan Publishing Company, New York.
US Department of Commerce (1979), Statistical Abstract of the United States. US Government Printing Office, Washington, DC.
## Willam H. Greene, Econometric Analysis, 2nd Ed. ## Chapter 14 ## load data set, p. 385, Table 14.1 data(PublicSchools) ## omit NA in Wisconsin and scale income ps <- na.omit(PublicSchools) ps$Income <- ps$Income * 0.0001 ## fit quadratic regression, p. 385, Table 14.2 fmq <- lm(Expenditure ~ Income + I(Income^2), data = ps) summary(fmq) ## compare standard and HC0 standard errors ## p. 391, Table 14.3 library(sandwich) coef(fmq) sqrt(diag(vcovHC(fmq, type = "const"))) sqrt(diag(vcovHC(fmq, type = "HC0"))) if(require(lmtest)) { ## compare t ratio coeftest(fmq, vcov = vcovHC(fmq, type = "HC0")) ## White test, p. 393, Example 14.5 wt <- lm(residuals(fmq)^2 ~ poly(Income, 4), data = ps) wt.stat <- summary(wt)$r.squared * nrow(ps) c(wt.stat, pchisq(wt.stat, df = 3, lower = FALSE)) ## Bresch-Pagan test, p. 395, Example 14.7 bptest(fmq, studentize = FALSE) bptest(fmq) ## Francisco Cribari-Neto, Asymptotic Inference, CSDA 45 ## quasi z-tests, p. 229, Table 8 ## with Alaska coeftest(fmq, df = Inf)[3,4] coeftest(fmq, df = Inf, vcov = vcovHC(fmq, type = "HC0"))[3,4] coeftest(fmq, df = Inf, vcov = vcovHC(fmq, type = "HC3"))[3,4] coeftest(fmq, df = Inf, vcov = vcovHC(fmq, type = "HC4"))[3,4] ## without Alaska (observation 2) fmq1 <- lm(Expenditure ~ Income + I(Income^2), data = ps[-2,]) coeftest(fmq1, df = Inf)[3,4] coeftest(fmq1, df = Inf, vcov = vcovHC(fmq1, type = "HC0"))[3,4] coeftest(fmq1, df = Inf, vcov = vcovHC(fmq1, type = "HC3"))[3,4] coeftest(fmq1, df = Inf, vcov = vcovHC(fmq1, type = "HC4"))[3,4] } ## visualization, p. 230, Figure 1 plot(Expenditure ~ Income, data = ps, xlab = "per capita income", ylab = "per capita spending on public schools") inc <- seq(0.5, 1.2, by = 0.001) lines(inc, predict(fmq, data.frame(Income = inc)), col = 4) fml <- lm(Expenditure ~ Income, data = ps) abline(fml) text(ps[2,2], ps[2,1], rownames(ps)[2], pos = 2)