# hccm

##### Heteroscedasticity-Corrected Covariance Matrices

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.

- Keywords
- regression

##### Usage

`hccm(model, ...)`# S3 method for lm
hccm(model, type=c("hc3", "hc0", "hc1", "hc2", "hc4"),
singular.ok=TRUE, ...)

# S3 method for default
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`

.

##### 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.

##### Value

The heteroscedasticity-corrected covariance matrix for the model.

##### References

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.

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

```
# NOT RUN {
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
# }
```

*Documentation reproduced from package car, version 3.0-10, License: GPL (>= 2)*