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 original 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 matrix.
The function hccm.default
simply catches non-lm
objects.
See Freedman (2006) and Fox and Weisberg (2019, Sec. 5.1.2) for discussion of the use of these methods in generalized linear models or models with nonconstant variance.
Value
The heteroscedasticity-corrected covariance matrix for the model.
The function will return an error, rather than a matrix, under two circumstances. First, if any of the cases have hatvalue (leverage) equal to one, then the corresponding fitted value will always equal the observed value. For types hc2, hc3 and hc4 the hccm matrix is undefined. For hc0 and hc1 it is defined but it can be shown to be singular, and therefore not a consistent estimate of the covariance matrix of the coefficient estimates. A singular estimate of the covariance matrix may also be obstained if the matrix X
is ill-conditioned. In this latter case rescaling the model matrix may give a full-rank estimate.
Author(s)
John Fox jfox@mcmaster.ca
References
Cribari-Neto, F. (2004) Asymptotic inference under heteroskedasticity of unknown form. Computational Statistics and Data Analysis 45, 215–233.
Fox, J. (2016) Applied Regression Analysis and Generalized Linear Models, Third Edition. Sage.
Fox, J. and Weisberg, S. (2019) An R Companion to Applied Regression, Third Edition, Sage.
Freedman, D. (2006) On the so-called "Huber sandwich estimator" and "robust standard errors", American Statistician, 60, 299–302.
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
mod <- lm(interlocks ~ assets + nation, data=Ornstein)
print(vcov(mod), digits=4)
## (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
print(hccm(mod), digits=4)
## (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