clusterSEs (version 2.6.2)

cluster.bs.glm: Pairs Cluster Bootstrapped p-Values For GLM

Description

This software estimates p-values using pairs cluster bootstrapped t-statistics for GLM models (Cameron, Gelbach, and Miller 2008). The data set is repeatedly re-sampled by cluster, a model is estimated, and inference is based on the sampling distribution of the pivotal (t) statistic.

Usage

cluster.bs.glm(mod, dat, cluster, ci.level = 0.95, boot.reps = 1000,
  stratify = FALSE, cluster.se = TRUE, report = TRUE,
  prog.bar = TRUE, output.replicates = FALSE, seed = NULL)

Arguments

mod

A model estimated using glm.

dat

The data set used to estimate mod.

cluster

A formula of the clustering variable.

ci.level

What confidence level should CIs reflect?

boot.reps

The number of bootstrap samples to draw.

stratify

Sample clusters only (= FALSE) or clusters and observations by cluster (= TRUE).

cluster.se

Use clustered standard errors (= TRUE) or ordinary SEs (= FALSE) for bootstrap replicates.

report

Should a table of results be printed to the console?

prog.bar

Show a progress bar of the bootstrap (= TRUE) or not (= FALSE).

output.replicates

Should the cluster bootstrap coefficient replicates be output (= TRUE) or not (= FALSE)?

seed

Random number seed for replicability (default is NULL).

Value

A list with the elements

p.values

A matrix of the estimated p-values.

ci

A matrix of confidence intervals.

replicates

Optional: A matrix of the coefficient estimates from each cluster bootstrap replicate.

References

Esarey, Justin, and Andrew Menger. 2017. "Practical and Effective Approaches to Dealing with Clustered Data." Political Science Research and Methods forthcoming: 1-35. <URL:http://jee3.web.rice.edu/cluster-paper.pdf>.

Cameron, A. Colin, Jonah B. Gelbach, and Douglas L. Miller. 2008. "Bootstrap-Based Improvements for Inference with Clustered Errors." The Review of Economics and Statistics 90(3): 414-427. <DOI:10.1162/rest.90.3.414>.

Examples

# NOT RUN {
##################################################################
# example one: predict whether respondent has a university degree
##################################################################
require(effects)
data(WVS)
logit.model <- glm(degree ~ religion + gender + age, data=WVS, family=binomial(link="logit"))
summary(logit.model)

# compute pairs cluster bootstrapped p-values
clust.bs.p <- cluster.bs.glm(logit.model, WVS, ~ country, report = T)

  
######################################
# example two: predict chicken weight
######################################
rm(list=ls())
data(ChickWeight)

dum <- model.matrix(~ ChickWeight$Diet)
ChickWeight$Diet2 <- as.numeric(dum[,2])
ChickWeight$Diet3 <- as.numeric(dum[,3])
ChickWeight$Diet4 <- as.numeric(dum[,4])

weight.mod2 <- glm(formula = weight~Diet2+Diet3+Diet4+log(Time+1),data=ChickWeight)

# compute pairs cluster bootstrapped p-values
clust.bs.w <- cluster.bs.glm(weight.mod2, ChickWeight, ~ Chick, report = T)


###################################################################
# example three: murder rate by U.S. state, with interaction term
###################################################################
rm(list=ls())
require(datasets)

state.x77.dat <- data.frame(state.x77)
state.x77.dat$Region <- state.region
state.x77.dat$IncomeXHS <- state.x77.dat$Income * state.x77.dat$HS.Grad
income.mod <- glm( Murder ~ Income + HS.Grad + IncomeXHS , data=state.x77.dat)

# compute pairs cluster bootstrapped p-values
clust.bs.inc <- cluster.bs.glm(income.mod, state.x77.dat, ~ Region, 
                               report = T, output.replicates=T, boot.reps=10000)

# compute effect of income on murder rate, by percentage of HS graduates
# using conventional standard errors
HS.grad.vec <- seq(from=38, to=67, by=1)
me.income <- coefficients(income.mod)[2] + coefficients(income.mod)[4]*HS.grad.vec
plot(me.income ~ HS.grad.vec, type="l", ylim=c(-0.0125, 0.0125), 
     xlab="% HS graduates", ylab="ME of income on murder rate")
se.income <- sqrt( vcov(income.mod)[2,2] + vcov(income.mod)[4,4]*(HS.grad.vec)^2 +
                   2*vcov(income.mod)[2,4]*HS.grad.vec )
ci.h <- me.income + qt(0.975, lower.tail=T, df=46) * se.income
ci.l <- me.income - qt(0.975, lower.tail=T, df=46) * se.income
lines(ci.h ~ HS.grad.vec, lty=2)
lines(ci.l ~ HS.grad.vec, lty=2)

# use pairs cluster bootstrap to compute CIs, including bootstrap bias-correction factor
# including bootstrap bias correction factor
# cluster on Region
################################################
# marginal effect replicates =
me.boot <- matrix(data = clust.bs.inc$replicates[,2], nrow=10000, ncol=30, byrow=F) +
           as.matrix(clust.bs.inc$replicates[,4]) %*% t(HS.grad.vec)
# compute bias-corrected MEs
me.income.bias.cor <- 2*me.income - apply(X=me.boot, FUN=mean, MARGIN=2)
# adjust bootstrap replicates for bias
me.boot.bias.cor <- me.boot + matrix(data = 2*(me.income - 
                                     apply(X=me.boot, FUN=mean, MARGIN=2)),
                                     ncol=30, nrow=10000, byrow=T)
# compute pairs cluster bootstrap 95% CIs, including bias correction
me.boot.plot <- apply(X = me.boot.bias.cor, FUN=quantile, MARGIN=2, probs=c(0.025, 0.975))
# plot bootstrap bias-corrected marginal effects
lines(me.income.bias.cor ~ HS.grad.vec, lwd=2)
# plot 95% Cis
# a little lowess smoothing applied to compensate for discontinuities 
# arising from shifting between replicates
lines(lowess(me.boot.plot[1,] ~ HS.grad.vec), lwd=2, lty=2)
lines(lowess(me.boot.plot[2,] ~ HS.grad.vec), lwd=2, lty=2)

# finishing touches to plot
legend(lty=c(1,2,1,2), lwd=c(1,1,2,2), "topleft", 
       legend=c("Model Marginal Effect", "Conventional 95% CI", 
                "BS Bias-Corrected Marginal Effect", "Cluster Bootstrap 95% CI"))

# }