36.4 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.