Robust standard errors

In a recent article in Multivariate Behavioral Research, we (Huang, Wiedermann, and Zhang; HWZ; doi: 10.¹⁰⁸⁰⁄_00273171.2022.2077290) discuss a robust standard error that can be used with mixed models that accounts for violations of homogeneity. Note that these robust standard errors have been around for years though are not always provided in statistical software. These can also be computed using the CR2 package or the clubSandwich package. This page shows how to compute the traditional Liang and Zeger (1986) robust standard errors (CR0) and the CR2 estimator- see Bell and McCaffrey (2002) as well as McCaffrey, Bell, and Botts (2001) (BM and MBB).