hccm | R Documentation |

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.

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

`model` |
a unweighted or weighted linear model, produced by |

`type` |
one of |

`singular.ok` |
if |

`...` |
arguments to pass to |

The original White-corrected coefficient covariance matrix (`"hc0"`

) for an unweighted model is

*V(b) = inv(X'X) X' diag(e^2) X inv(X'X)*

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.

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.

The heteroscedasticity-corrected covariance matrix will be singular if one or more observations have hatvalues (leverages) equal to 1, and hence is not a consistent estimate of the population covariance matrix. This will occur most often in outlier testing: if there are m suspected outliers then m dummy variables are added to the regression model corresponding to the m cases (See Section 2.2.2 of Cook and Weisberg (1982)). The function returns an error if the heteroscedasticity-corrected covariance matrix is singular.

The heteroscedasticity-corrected covariance matrix for the model.

John Fox jfox@mcmaster.ca

Cook, R. D. and Weisberg, S. (1982). Residuals and Influence in Regression, Chapman and Hall, https://hdl.handle.net/11299/37076.

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.

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

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