38.4 Standard Errors

sandwich vignette

Type Applicable Usage Reference
const Assume constant variances
HC HC0 vcovCL

Heterogeneity

White’s estimator

All other heterogeneity SE methods are derivatives of this.

No small sample bias adjustment

(White 1980)
HC1 vcovCL

Uses a degrees of freedom-based correction

When the number of clusters is small, HC2 and HC3 are better (Cameron, Gelbach, and Miller 2008)

(J. G. MacKinnon and White 1985)
HC2 vcovCL

Better with the linear model, but still applicable for Generalized Linear Models

Needs a hat (weighted) matrix

HC3 vcovCL

Better with the linear model, but still applicable for Generalized Linear Models

Needs a hat (weighted) matrix

HC4 vcovHC (Cribari-Neto 2004)
HC4m vcovHC (Cribari-Neto, Souza, and Vasconcellos 2007)
HC5 vcovHC (Cribari-Neto and Silva 2011)
data(cars)
model <- lm(speed ~ dist, data = cars)
summary(model)
#> 
#> Call:
#> lm(formula = speed ~ dist, data = cars)
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -7.5293 -2.1550  0.3615  2.4377  6.4179 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)  8.28391    0.87438   9.474 1.44e-12 ***
#> dist         0.16557    0.01749   9.464 1.49e-12 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 3.156 on 48 degrees of freedom
#> Multiple R-squared:  0.6511, Adjusted R-squared:  0.6438 
#> F-statistic: 89.57 on 1 and 48 DF,  p-value: 1.49e-12
lmtest::coeftest(model, vcov. = sandwich::vcovHC(model, type = "HC1"))
#> 
#> t test of coefficients:
#> 
#>             Estimate Std. Error t value  Pr(>|t|)    
#> (Intercept) 8.283906   0.891860  9.2883 2.682e-12 ***
#> dist        0.165568   0.019402  8.5335 3.482e-11 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

References

Cameron, A Colin, Jonah B Gelbach, and Douglas L Miller. 2008. “Bootstrap-Based Improvements for Inference with Clustered Errors.” The Review of Economics and Statistics 90 (3): 414–27.
Cribari-Neto, Francisco. 2004. “Asymptotic Inference Under Heteroskedasticity of Unknown Form.” Computational Statistics & Data Analysis 45 (2): 215–33.
Cribari-Neto, Francisco, and Wilton Bernardino da Silva. 2011. “A New Heteroskedasticity-Consistent Covariance Matrix Estimator for the Linear Regression Model.” AStA Advances in Statistical Analysis 95: 129–46.
Cribari-Neto, Francisco, Tatiene C Souza, and Klaus LP Vasconcellos. 2007. “Inference Under Heteroskedasticity and Leveraged Data.” Communications in Statistics—Theory and Methods 36 (10): 1877–88.
MacKinnon, James G, and Halbert White. 1985. “Some Heteroskedasticity-Consistent Covariance Matrix Estimators with Improved Finite Sample Properties.” Journal of Econometrics 29 (3): 305–25.
White, Halbert. 1980. “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity.” Econometrica: Journal of the Econometric Society, 817–38.