R: Heteroscedasticity-Corrected Covariance Matrices

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 `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 classical 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.

### 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.

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

[Package car version 2.1-4 Index]