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lm_clustered_se.r
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lm_clustered_se.r
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# Code for Economic Theory Blog
#
# economictheoryblog.com
#
# August 2016
# a.d.
summary.lm.clustered <- function (object, correlation = FALSE,
symbolic.cor = FALSE, robust=FALSE,
cluster=c(NULL,NULL),...) {
# Make sure the call is a formula
object$call$formula = as.formula(object$call$formula)
# add extension for robust standard errors
if(robust==TRUE){
# save variable that are necessary to calcualte robust sd
X <- model.matrix(object)
u2 <- residuals(object)^2
XDX <- 0
## One needs to calculate X'DX. But due to the fact that
## D is huge (NxN), it is better to do it with a cycle.
for(i in 1:nrow(X)) {
XDX <- XDX + u2[i]*X[i,]%*%t(X[i,])
}
# inverse(X'X)
XX1 <- solve(t(X)%*%X,tol = 1e-100)
# Sandwich Variance calculation (Bread x meat x Bread)
varcovar <- XX1 %*% XDX %*% XX1
# adjust degrees of freedom
dfc_r <- sqrt(nrow(X))/sqrt(nrow(X)-ncol(X))
# Standard errors of the coefficient estimates are the
# square roots of the diagonal elements
rstdh <- dfc_r*sqrt(diag(varcovar))
}
# add extension for clustered standard errors
if(!is.null(cluster)&robust==T){warning("Robust standard errors are calculated. Set robust=F to calculate clustered standard errors.")}
if(!is.null(cluster)&robust==F){
if(""%in%cluster){stop("No variable for clustering provided.")}
if(length(cluster)>2){stop("The function only allows max. 2 clusters. You provided more.")}
n_coef <- all.vars(object$call$formula)
if(length(cluster)==1){
dat <- na.omit(get(paste(object$call$data))[,c(n_coef,cluster)])
if(nrow(dat)<nrow(object$model)){stop("Not all observation have a cluster.")}
cluster <- dat[,cluster]
require(sandwich, quietly = TRUE)
M <- res_length <- length(unique(cluster))
N <- length(cluster)
K <- object$rank
dfc <- (M/(M-1))*((N-1)/(N-K))
uj <- na.omit(apply(estfun(object),2, function(x) tapply(x, cluster, sum)));
varcovar <- dfc*sandwich(object, meat=crossprod(uj)/N)
rstdh <- sqrt(diag(varcovar))
}
if(length(cluster)==2){
dat_1 <- na.omit(get(paste(object$call$data))[,c(n_coef,cluster[1])])
if(nrow(dat_1)<nrow(object$model)){stop("Not all observation have a cluster.")}
dat_2 <- na.omit(get(paste(object$call$data))[,c(n_coef,cluster[2])])
if(nrow(dat_2)<nrow(object$model)){stop("Not all observation have a cluster.")}
dat <- na.omit(get(paste(object$call$data))[,c(n_coef,cluster)])
library(sandwich,quietly = TRUE)
cluster1 <- dat[,cluster[1]]
cluster2 <- dat[,cluster[2]]
cluster12 = paste(cluster1,cluster2, sep="")
M1 <- length(unique(cluster1))
M2 <- length(unique(cluster2))
M12 <- res_length <-length(unique(cluster12))
N <- length(cluster1)
K <- object$rank
dfc1 <- (M1/(M1-1))*((N-1)/(N-K))
dfc2 <- (M2/(M2-1))*((N-1)/(N-K))
dfc12 <- (M12/(M12-1))*((N-1)/(N-K))
u1j <- apply(estfun(object), 2, function(x) tapply(x, cluster1, sum))
u2j <- apply(estfun(object), 2, function(x) tapply(x, cluster2, sum))
u12j <- apply(estfun(object), 2, function(x) tapply(x, cluster12, sum))
vc1 <- dfc1*sandwich(object, meat=crossprod(u1j)/N )
vc2 <- dfc2*sandwich(object, meat=crossprod(u2j)/N )
vc12 <- dfc12*sandwich(object, meat=crossprod(u12j)/N)
varcovar <- vc1 + vc2 - vc12
rstdh <- sqrt(diag(varcovar))
}
}
z <- object
p <- z$rank
rdf <- z$df.residual
if (p == 0) {
r <- z$residuals
n <- length(r)
w <- z$weights
if (is.null(w)) {
rss <- sum(r^2)
}
else {
rss <- sum(w * r^2)
r <- sqrt(w) * r
}
resvar <- rss/rdf
ans <- z[c("call", "terms", if (!is.null(z$weights)) "weights")]
class(ans) <- "summary.lm"
ans$aliased <- is.na(coef(object))
ans$residuals <- r
ans$df <- c(0L, n, length(ans$aliased))
ans$coefficients <- matrix(NA, 0L, 4L)
dimnames(ans$coefficients) <- list(NULL, c("Estimate",
"Std. Error", "t value", "Pr(>|t|)"))
ans$sigma <- sqrt(resvar)
ans$r.squared <- ans$adj.r.squared <- 0
return(ans)
}
if (is.null(z$terms))
stop("invalid 'lm' object: no 'terms' component")
if (!inherits(object, "lm"))
warning("calling summary.lm(<fake-lm-object>) ...")
Qr <- stats:::qr.lm(object)
n <- NROW(Qr$qr)
if (is.na(z$df.residual) || n - p != z$df.residual)
warning("residual degrees of freedom in object suggest this is not an \"lm\" fit")
r <- z$residuals
f <- z$fitted.values
w <- z$weights
if (is.null(w)) {
mss <- if (attr(z$terms, "intercept"))
sum((f - mean(f))^2)
else sum(f^2)
rss <- sum(r^2)
}
else {
mss <- if (attr(z$terms, "intercept")) {
m <- sum(w * f/sum(w))
sum(w * (f - m)^2)
}
else sum(w * f^2)
rss <- sum(w * r^2)
r <- sqrt(w) * r
}
resvar <- rss/rdf
if (is.finite(resvar) && resvar < (mean(f)^2 + var(f)) *
1e-30)
warning("essentially perfect fit: summary may be unreliable")
p1 <- 1L:p
R <- chol2inv(Qr$qr[p1, p1, drop = FALSE])
se <- sqrt(diag(R) * resvar)
if(robust==T){se <- rstdh}
if(!is.null(cluster)&robust==F){se <- rstdh}
est <- z$coefficients[Qr$pivot[p1]]
tval <- est/se
ans <- z[c("call", "terms", if (!is.null(z$weights)) "weights")]
ans$residuals <- r
pval <- 2 * pt(abs(tval),
rdf, lower.tail = FALSE)
ans$coefficients <- cbind(est, se, tval, pval)
dimnames(ans$coefficients) <- list(names(z$coefficients)[Qr$pivot[p1]],
c("Estimate", "Std. Error", "t value", "Pr(>|t|)"))
ans$aliased <- is.na(coef(object))
ans$sigma <- sqrt(resvar)
ans$df <- c(p, rdf, NCOL(Qr$qr))
if (p != attr(z$terms, "intercept")) {
df.int <- if (attr(z$terms, "intercept"))
1L
else 0L
ans$r.squared <- mss/(mss + rss)
ans$adj.r.squared <- 1 - (1 - ans$r.squared) * ((n -
df.int)/rdf)
ans$fstatistic <- c(value = (mss/(p - df.int))/resvar,
numdf = p - df.int, dendf = rdf)
if(robust==T|(!is.null(cluster))){
if(!is.null(cluster)){rdf <- res_length -1}
pos_coef <- match(names(z$coefficients)[-match("(Intercept)",
names(z$coefficients))],
names(z$coefficients))
P_m <- matrix(z$coefficients[pos_coef])
R_m <- diag(1,
length(pos_coef),
length(pos_coef))
ans$fstatistic <- c(value = t(R_m%*%P_m)%*%
(solve(varcovar[pos_coef,pos_coef],tol = 1e-100))%*%
(R_m%*%P_m)/(p - df.int),
numdf = p - df.int, dendf = rdf)
}
}
else ans$r.squared <- ans$adj.r.squared <- 0
ans$cov.unscaled <- R
dimnames(ans$cov.unscaled) <- dimnames(ans$coefficients)[c(1,
1)]
if (correlation) {
ans$correlation <- (R * resvar)/outer(se, se)
dimnames(ans$correlation) <- dimnames(ans$cov.unscaled)
ans$symbolic.cor <- symbolic.cor
}
if (!is.null(z$na.action))
ans$na.action <- z$na.action
ans$varcovar = varcovar
class(ans) <- "summary.lm"
ans
}