vcovHC(x, ...)## S3 method for class 'default':
vcovHC(x,
type = c("HC3", "const", "HC", "HC0", "HC1", "HC2", "HC4"),
omega = NULL, sandwich = TRUE, ...)
meatHC(x, type = , omega = NULL)
residuals
(the working residuals of the model), diaghat (the diagonal
of the corresponding hat matrix) and df (the residual degrees of
freedom). FALSE only the meat matrix is returned.sandwich.meatHC is the real work horse for estimating
the meat of HC sandwich estimators -- the default vcovHC method
is a wrapper calling
sandwich and bread. See Zeileis (2006) for
more implementation details. The theoretical background, exemplified
for the linear regression model, is described below and in Zeileis (2004). When type = "const" constant variances are assumed and
and vcovHC gives the usual estimate of the covariance matrix of
the coefficient estimates:
$$\hat \sigma^2 (X^\top X)^{-1}$$
All other methods do not assume constant variances and are suitable in case of
heteroskedasticity. "HC" (or equivalently "HC0") gives White's
estimator, the other estimators are refinements of this. They are all of form
$$(X^\top X)^{-1} X^\top \Omega X (X^\top X)^{-1}$$
and differ in the choice of Omega. This is in all cases a diagonal matrix whose
elements can be either supplied as a vector omega or as a
a function omega of the residuals, the diagonal elements of the hat matrix and
the residual degrees of freedom. For White's estimator
omega <- function(residuals, diaghat, df) residuals^2
Instead of specifying of providing the diagonal omega or a function for
estimating it, the type argument can be used to specify the
HC0 to HC4 estimators. If omega is used, type is ignored.
Long & Ervin (2000) conduct a simulation study of HC estimators in
the linear regression model, recommending to use HC3 which is thus the
default in vcovHC. Cribari-Neto (2004) suggests the HC4 type
estimator which is tailored to take into account the effect of leverage
points in the design matrix. For more details see the references.
Long J. S., Ervin L. H. (2000), Using Heteroscedasticity Consistent Standard Errors in the Linear Regression Model. The American Statistician, 54, 217--224.
MacKinnon J. G., White H. (1985), Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties. Journal of Econometrics 29, 305--325.
White H. (1980), A heteroskedasticity-consistent covariance matrix and a direct test for heteroskedasticity. Econometrica 48, 817--838.
Zeileis A (2004), Econometric Computing with HC and HAC Covariance Matrix
Estimators. Journal of Statistical Software, 11(10), 1--17.
URL
Zeileis A (2006), Object-oriented Computation of Sandwich Estimators.
Journal of Statistical Software, 16(9), 1--16.
URL
lm, hccm,
bptest, ncv.test## generate linear regression relationship
## with homoskedastic variances
x <- sin(1:100)
y <- 1 + x + rnorm(100)
## model fit and HC3 covariance
fm <- lm(y ~ x)
vcovHC(fm)
## usual covariance matrix
vcovHC(fm, type = "const")
vcov(fm)
sigma2 <- sum(residuals(lm(y ~ x))^2)/98
sigma2 * solve(crossprod(cbind(1, x)))Run the code above in your browser using DataLab