Re: heteroskedasticity-consistent (HC) standard errors
Posted: Mon Mar 08, 2021 9:44 am
Ok...thanks for all your help. I have made progress, and now get output with robust SEs, but I still have a few questions.
@jonathon I put on its own line at the end. But as you can see from my code below, there is a LOT of syntax to run here. And also the commands build on a Stata dataset. If I want my undergrads to do this, I was hoping (a) the syntax could be much more concise, and (b) they could start from their own .omv dataset they have ben using. Any thoughts on these issues?
Code below:
@jonathon I put
Code: Select all
my_modelCode below:
Code: Select all
summary.lm <- function (object, correlation = FALSE,
symbolic.cor = FALSE, robust=FALSE,
cluster=c(NULL,NULL),...) {
# 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$model)){stop("Not all observation have a cluster.")}
cluster_vector <- dat[,cluster]
require(sandwich, quietly = TRUE)
M <- res_length <- length(unique(cluster_vector))
N <- length(cluster_vector)
K <- object$rank
dfc <- (M/(M-1))*((N-1)/(N-K))
uj <- na.omit(apply(estfun(object),2, function(x) tapply(x, cluster_vector, 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
class(ans) <- "summary.lm"
ans
}
# --------------------------------------------------------------------------- #
library(haven)
library(lmtest)
# Import Stata file
my_data <- read_dta('/Users/tk1/Dropbox/teaching/BUS135_QUANT/data/lab_data_baseline.dta')
my_model <- lm(grsswk ~ sexx + ttushr + sc10mmj, data = my_data)
my_model
summary(my_model) # non-robust Std. Error
# new summary()
summary(my_model, robust=T) # robust Std. Error
there is a lot of code there, but maybe i can help with the little bit i think i understand.