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#' Wild Cluster Bootstrapped p-Values For PLM
#'
#' This software estimates p-values using wild cluster bootstrapped t-statistics for fixed effects panel linear models (Cameron, Gelbach, and Miller 2008). Residuals are repeatedly re-sampled by cluster to form a pseudo-dependent variable, a model is estimated for each re-sampled data set, and inference is based on the sampling distribution of the pivotal (t) statistic. The null is never imposed for PLM models.
#'
#' @param mod A "within" model estimated using \code{plm}.
#' @param dat The data set used to estimate \code{mod}.
#' @param cluster Clustering dimension ("group", the default, or "time").
#' @param ci.level What confidence level should CIs reflect? (Note: only reported when \code{impose.null == FALSE}).
#' @param boot.reps The number of bootstrap samples to draw.
#' @param report Should a table of results be printed to the console?
#' @param prog.bar Show a progress bar of the bootstrap (= TRUE) or not (= FALSE).
#' @param output.replicates Should the cluster bootstrap coefficient replicates be output (= TRUE) or not (= FALSE)?
#' @param seed Random number seed for replicability (default is NULL).
#'
#' @return A list with the elements
#' \item{p.values}{A matrix of the estimated p-values.}
#' \item{ci}{A matrix of confidence intervals (if null not imposed).}
#' @author Justin Esarey
#' @examples
#' \dontrun{
#'
#' # predict employment levels, cluster on group
#' require(plm)
#' data(EmplUK)
#'
#' emp.1 <- plm(emp ~ wage + log(capital+1), data = EmplUK, model = "within",
#' index=c("firm", "year"))
#' cluster.wild.plm(mod=emp.1, dat=EmplUK, cluster="group", ci.level = 0.95,
#' boot.reps = 1000, report = TRUE, prog.bar = TRUE)
#'
#' # cluster on time
#' cluster.wild.plm(mod=emp.1, dat=EmplUK, cluster="time", ci.level = 0.95,
#' boot.reps = 1000, report = TRUE, prog.bar = TRUE)
#'
#' }
#' @rdname cluster.wild.plm
#' @import plm
#' @import Formula
#' @references Esarey, Justin, and Andrew Menger. 2017. "Practical and Effective Approaches to Dealing with Clustered Data." \emph{Political Science Research and Methods} forthcoming: 1-35. <URL:http://jee3.web.rice.edu/cluster-paper.pdf>.
#' @references Cameron, A. Colin, Jonah B. Gelbach, and Douglas L. Miller. 2008. "Bootstrap-Based Improvements for Inference with Clustered Errors." \emph{The Review of Economics and Statistics} 90(3): 414-427. <DOI:10.1162/rest.90.3.414>.
#' @import stats
#' @importFrom utils write.table
#' @importFrom utils setTxtProgressBar
#' @importFrom utils txtProgressBar
#' @export
#'
cluster.wild.plm<-function(mod, dat, cluster, ci.level = 0.95, boot.reps = 1000,
report = TRUE, prog.bar = TRUE, output.replicates = FALSE,
seed=NULL){
# compensate for bizarre R formula updating bug
# thanks to Jason Thorpe for reporting!
form.old <- update(mod$formula, 1 ~ 1 )
while(form.old != mod$formula){
form.old <- mod$formula
invisible(mod <- update(mod, formula = .~.))
}
if(is.null(seed)==F){ # if user supplies a seed, set it
tryCatch(set.seed(seed),
error = function(e){return("seed must be a valid integer")},
warning = function(w){return(NA)})
}
if( min( class(dat) != "pdata.frame" ) ){ # if data not pdata.frame
# print a warning about auto-conversion of data
cat("\n", "\n", "Note: auto-converting data to pdata.frame; first two variables MUST be group and time indices.", "\n",
"See ?pdata.frame and consider manually converting data to pdata.frame.", "\n", "\n")
dat <- pdata.frame(dat, index=colnames(dat)[1:2], row.names=F) # convert it
}
if(cluster=="group"){
clust <- attr(mod$mod, "index")[,1] # which clusters were used?
clust.name <- colnames(attr(mod$mod, "index"))[1] # what is the name of the cluster?
clust.full <- attr(dat, "index")[,1] # all clusters in the dataset
used.idx <- which(rownames(dat) %in% rownames(mod$model)) # what were the actively used observations in the model?
G<-length(unique(clust)) # how many clusters are in this model?
}
if(cluster=="time"){
cat("\n", "\n", "Note: create new variable containing lag when clustering on time", "\n")
clust <- attr(mod$mod, "index")[,2] # which clusters were used?
clust.name <- colnames(attr(mod$mod, "index"))[2] # what is the name of the cluster?
clust.full <- attr(dat, "index")[,2] # all clusters in the dataset
used.idx <- which(rownames(dat) %in% rownames(mod$model)) # what were the actively used observations in the model?
G<-length(unique(clust)) # how many clusters are in this model?
}
if(cluster != "group" & cluster != "time"){
stop("invalid clustering variable; see help file")
}
"%w/o%" <- function(x, y) x[!x %in% y] # a little function to create a without function (see ?match)
form <- mod$formula # what is the formula of this model?
variables <- all.vars(form) # what variables are in this model?
ind.variables.data <- all.vars(update(form, 1 ~ .)) # RHS variables in this model
ind.variables <- rownames(summary(mod)$coefficients) # what independent variables are in this model?
count.v <- dim(mod$model)[2]
ind.variables.full <- colnames(mod$model)[2:count.v] # what independent variables (incld drops, but not intercept) are in this model?
ind.variables.name <- ind.variables %w/o% "(Intercept)" # what independent variables (excld intercept) are in this model?
se.clust <- sqrt(diag(vcovHC(mod, cluster=cluster))) # retrieve the clustered SEs
beta.mod <- coefficients(mod)[ind.variables] # retrieve the estimated coefficients
w <- beta.mod / se.clust # calculate the t-test statistic
# in case dv is wrapped in a function, need to set it to its functional value
# so that residuals can be added w/o incident
dat$dv.new[used.idx] <- mod$model[,1] # add transformed DV into data set
form.new <- update(form, dv.new ~ .) # substitute in new dV
if(prog.bar==TRUE){cat("Wild Cluster bootstrapping w/o imposing null...", "\n")}
boot.dat <- dat # copy the data set into a bootstrap resampling dataset
w.store <- matrix(data=NA, nrow=boot.reps,
ncol=length(ind.variables)) # store bootstrapped test statistics
# keep track of the beta bootstrap replicates for possible output
rep.store <- matrix(data=NA, nrow=boot.reps, ncol=length(beta.mod))
colnames(rep.store) <- ind.variables
resid <- residuals(mod) # get the residuals for the model
if(prog.bar==TRUE){pb <- txtProgressBar(min = 0, max = boot.reps, initial = 0, style = 3)}
for(i in 1:boot.reps){
if(prog.bar==TRUE){setTxtProgressBar(pb, value=i)}
weight <- c(1, -1)[rbinom(G, size=1, prob=0.5) # assign wild bootstrap weights
+ 1][match(clust, unique(clust))]
pseudo.resid <- resid*weight # create pseudo-residuals using weights
pseudo.dv <- predict(mod)+ pseudo.resid # create pseudo-observations using pseudo-residuals
boot.dat[used.idx,"dv.new"] <- pseudo.dv # create a bootstrap replicate data set (note dv.new)
boot.mod.call <- mod$call # retrieve the original model call
boot.mod.call[[2]] <- quote(form.new) # use formula with transformed DV
boot.mod.call[[3]] <- quote(boot.dat) # use bootstrap data set
boot.mod <- suppressWarnings(tryCatch(eval(boot.mod.call), # attempt to re-run the model
error = function(e){return(NA)}))
se.boot <- sqrt(diag(vcovHC(boot.mod, cluster=cluster))) # retrieve the bootstrap clustered SE
beta.boot <- coefficients(boot.mod)[ind.variables] # store the bootstrap beta coefficient
w.store[i,] <- (beta.boot-beta.mod) / se.boot # store the bootstrap test statistic
rep.store[i,] <- beta.boot # store the bootstrap beta for output
}
if(prog.bar==TRUE){close(pb)}
# Note: thanks to Mortiz Marbach for providing a bug fix to this section!
comp.fun<-function(vec2, vec1){as.numeric(vec1>vec2)} # a simple function comparing v1 to v2
if ( length(ind.variables)==1 ){
p.store.s <- matrix(as.double(abs(w)) > as.double(abs(w.store)), ncol=1) # compare the BS test stats to orig. result
crit.t <- quantile(abs(w.store),ci.level) # compute critical t-statistics for CIs
} else {
p.store.s <- t(apply(X = abs(w.store), FUN = comp.fun, MARGIN = 1, vec1 = abs(w))) # compare the BS test stats to orig. result
crit.t <- apply(X = abs(w.store), MARGIN = 2, FUN = quantile, probs = ci.level) # compute critical t-statistics for CIs
}
if(dim(p.store.s)[1] == 1){
p.store <- 1 - ( sum(p.store.s) / boot.reps ) # calculate the cluster bootstrap p-value
}else{
p.store <- 1 - ( colSums(p.store.s) / boot.reps ) # calculate the cluster bootstrap p-value
}
# compute confidence bounds
ci.lo <- beta.mod - crit.t*se.clust
ci.hi <- beta.mod + crit.t*se.clust
print.ci <- cbind(ind.variables, ci.lo, ci.hi)
print.ci <- rbind(c("variable name", "CI lower", "CI higher"), print.ci)
out.ci <- cbind(ci.lo, ci.hi)
rownames(out.ci) <- ind.variables
colnames(out.ci) <- c("CI lower", "CI higher")
out <- matrix(p.store, ncol=1)
colnames(out) <- c("wild cluster BS p-value")
rownames(out) <- ind.variables
out.p <- cbind(ind.variables, round(out, 3))
out.p <- rbind(c("variable name", "wild cluster BS p-value"), out.p)
printmat <- function(m){
write.table(format(m, justify="right"), row.names=F, col.names=F, quote=F, sep = " ")
}
if(report==T){
cat("\n", "\n", "Wild Cluster Bootstrapped p-values: ", "\n", "\n")
printmat(out.p)
if(is.null(print.ci) == FALSE){
cat("\n", "Confidence Intervals (derived from bootstrapped t-statistics): ", "\n", "\n")
printmat(print.ci)
}
if(length(ind.variables.name) < length(ind.variables.full)){
cat("\n", "\n", "****", "Note: ", length(ind.variables.full) - length(ind.variables.name), " variables were unidentified in the model and are not reported.", "****", "\n", sep="")
cat("Variables not reported:", "\n", sep="")
cat(ind.variables.full[!ind.variables.full %in% ind.variables.name], sep=", ")
cat("\n", "\n")
}
}
out.list<-list()
out.list[["p.values"]]<-out
out.list[["ci"]] <- out.ci
if(output.replicates == TRUE){out.list[["replicates"]] <- rep.store}
return(invisible(out.list))
}
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