vcovHC {sandwich} | R Documentation |
Heteroskedasticity-consistent estimation of the covariance matrix of the coefficient estimates in a linear regression model.
vcovHC(x, type = c("HC3", "const", "HC", "HC0", "HC1", "HC2", "HC4"), omega = NULL, ...)
x |
a fitted model object of class "lm" . |
type |
a character string specifying the estimation type. For details see below. |
omega |
a vector or a
function depending on the arguments residuals
(the residuals of the linear model), diaghat (the diagonal
of the corresponding hat matrix) and df (the residual degrees of
freedom). For details see below. |
... |
currently not used. |
When type = "const"
constant variances are assumed and
and vcovHC
gives the usual estimate of the covariance matrix of
the coefficient estimates:
sigma^2 (X'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'X)^{-1} X' Omega X (X'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.
For details see the references.
A matrix containing the covariance matrix estimate.
Cribari-Neto F. (2004), Asymptotic inference under heteroskedasticity of unknown form. Computational Statistics & Data Analysis 45, 215–233.
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.
## generate linear regression relationship ## with homoskedastic variances x <- sin(1:100) y <- 1 + x + rnorm(100) ## compute usual covariance matrix of coefficient estimates fm <- lm(y ~ x) vcovHC(fm, type="const") vcov(fm) sigma2 <- sum(residuals(lm(y~x))^2)/98 sigma2 * solve(crossprod(cbind(1,x)))