hccm {car} | R Documentation |
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, ...)
## S3 method for class 'lm'
hccm(model, type=c("hc3", "hc0", "hc1", "hc2", "hc4"),
singular.ok=TRUE, ...)
## Default S3 method:
hccm(model, ...)
Arguments
model |
a unweighted or weighted linear model, produced by |
type |
one of |
singular.ok |
if |
... |
arguments to pass to |
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_{i}^{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 amtrix.
The function hccm.default
simply catches non-lm
objects.
Value
The heteroscedasticity-corrected covariance matrix for the model.
Author(s)
John Fox jfox@mcmaster.ca
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. http://www.jstor.org/stable/2685594
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