Robust Standard Errors

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Computes standard errors that are robust to violations of the assumption of constant variance in regression and related models (i.e., heteroscedasticity). By default, the HC3 modification of White's (1980) estimator (Long and Ervin, 2000) is used (i.e., this is a sandwich estimator). Alternative options available when editing the code are HC1, HC2, and HC4.

Where weights are applied, this setting is ignored, as weights already employ a sandwich estimator.

The HC2, HC3 (default) and HC4 modifications can have singularities when one of the observations in the regression model has a hat value of one. This is since the modifications divide by a term involving one minus the hat values (division by zero). To avoid this singularity, if a regression model is fitted in this scenario, the observations with singularities are adjusted using HC2 which is a simple using the degrees of freedom (sample size minus the number of parameters). The observations without singularities are still computed using the requested HC2--HC4 otherwise.


Fox, John and Sanford Weisberg (2011). An {R} Companion to Applied Regression. Second Edition. Sage, Thousand Oaks,

Long, J. S. and Ervin, L. H. (2000). Using heteroscedasticity consistent standard errors in the linear regression model. The American Statistician, 54( 3): 217-224.

White, H. (1980), A heteroskedastic-consistent covariance matrix estimator and a direct test of heteroskedasticity.Econometrica, 48, 817-838.