sandwich (version 0.1-2)

vcovHC: Heteroskedasticity-Consistent Covariance Matrix Estimation

Description

Heteroskedasticity-consistent estimation of the covariance matrix of the coefficient estimates in a linear regression model.

Usage

vcovHC(x, order.by = NULL, data = list(),
  type = c("HC3", "const", "HC", "HC0", "HC1", "HC2", "HC4"),
  omega = NULL)

Arguments

x

a fitted model object of class "lm".

order.by

formula. A formula with a single explanatory variable like ~ x. The observations in the model are ordered by the size of x. If set to NULL (the default) the observations are assumed to be ordered (e.g. a

data

an optional data frame containing the variables in the order.by model. By default the variables are taken from the environment which vcovHC is called from.

type

a character string specifying the estimation type. For details see below.

omega

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 be

Value

• A matrix containing the covariance matrix estimate.

Details

When type = "const" constant variances are assumed and and covHC 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 are function 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 a type the argument omega can also be specified directly. For details see the references.

References

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.

See Also

lm, hccm, bptest, ncv.test

Examples

## 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)))