car (version 2.1-3)

hccm: Heteroscedasticity-Corrected Covariance Matrices

Description

Calculates heteroscedasticity-corrected covariance matrices linear models fit by least squares or weighted least squares. These are also called “White-corrected” or “White-Huber” covariance matrices.

Usage

hccm(model, ...)
"hccm"(model, type=c("hc3", "hc0", "hc1", "hc2", "hc4"), 
	singular.ok=TRUE, ...)
"hccm"(model, ...)

Arguments

model

a unweighted or weighted linear model, produced by lm.

type

one of "hc0", "hc1", "hc2", "hc3", or "hc4"; the first of these gives the classic White correction. The "hc1", "hc2", and "hc3" corrections are described in Long and Ervin (2000); "hc4" is described in Cribari-Neto (2004).

singular.ok

if FALSE (the default is TRUE), a model with aliased coefficients produces an error; otherwise, the aliased coefficients are ignored in the coefficient covariance matrix that's returned.

...

arguments to pass to hccm.lm.

Value

The heteroscedasticity-corrected covariance matrix for the model.

Details

The classical White-corrected coefficient covariance matrix ("hc0") (for an unweighted model) is $$V(b)=(X^{\prime }X{)}^{-1}{X}^{\prime }diag(e_i^2)X(X^{\prime }X{)}^{-1}$$ where $e^2$ are the squared residuals, and $X$ is the model matrix. The other methods represent adjustments to this formula. If there are weights, these are incorporated in the corrected covariance matrix. The function hccm.default simply catches non-lm objects.

References

Fox, J. (2008) Applied Regression Analysis and Generalized Linear Models, Second Edition. Sage. Fox, J. and Weisberg, S. (2011) An R Companion to Applied Regression, Second Edition, Sage.

Cribari-Neto, F. (2004) Asymptotic inference under heteroskedasticity of unknown form. Computational Statistics and Data Analysis 45, 215--233. Long, J. S. and Ervin, L. H. (2000) Using heteroscedasity consistent standard errors in the linear regression model. The American Statistician 54, 217--224. White, H. (1980) A heteroskedastic consistent covariance matrix estimator and a direct test of heteroskedasticity. Econometrica 48, 817--838.

Examples

options(digits=4)
mod<-lm(interlocks~assets+nation, data=Ornstein)
vcov(mod)
##             (Intercept)     assets  nationOTH   nationUK   nationUS
## (Intercept)   1.079e+00 -1.588e-05 -1.037e+00 -1.057e+00 -1.032e+00
## assets       -1.588e-05  1.642e-09  1.155e-05  1.362e-05  1.109e-05
## nationOTH    -1.037e+00  1.155e-05  7.019e+00  1.021e+00  1.003e+00
## nationUK     -1.057e+00  1.362e-05  1.021e+00  7.405e+00  1.017e+00
## nationUS     -1.032e+00  1.109e-05  1.003e+00  1.017e+00  2.128e+00
hccm(mod)             
##             (Intercept)     assets  nationOTH   nationUK   nationUS
## (Intercept)   1.664e+00 -3.957e-05 -1.569e+00 -1.611e+00 -1.572e+00
## assets       -3.957e-05  6.752e-09  2.275e-05  3.051e-05  2.231e-05
## nationOTH    -1.569e+00  2.275e-05  8.209e+00  1.539e+00  1.520e+00
## nationUK     -1.611e+00  3.051e-05  1.539e+00  4.476e+00  1.543e+00
## nationUS     -1.572e+00  2.231e-05  1.520e+00  1.543e+00  1.946e+00