Cluster Robust Standard Errors

Accounting for random slopes using cluster robust standard errors

Including random slopes (when warranted) in multilevel models is necessary to avoid making Type I errors as a result of underestimated standard errors. We typically investigate the presence of random slopes (RS) by using a likelihood ratio test and comparing two competing models. Often, random slopes are included when we have cross level interactions. If a random intercept (RI) model is used when a random slope model is warranted, the regression coefficients will be the same though the standard errors will be incorrect.

Jan 6, 2026

When Cluster-robust Inferences Fail

Although CRSEs are commonly-used, there are many instances where they can fail.

Nov 8, 2025

Accounting for random slopes using cluster-robust standard errors in multilevel models

Robust standard errors provide a convenient way to account for random slopes in multilevel models. They can also function as a diagnostic to test for the presence of random slopes.

Oct 8, 2025

More efficient CR2 cluster-robust standard errors

I had written before about using the CR2 standard error variant and how they can be used to account for clustering when using basic OLS (or GLM) regression. Some articles on the topic:

Oct 3, 2025

Cluster-robust standard errors with three-level data

Feb 1, 2025

Investigating the use of robust standard errors to account for two-way clustering in cross-classified data structures

Jan 1, 2024

Using cluster robust standard errors to analyze nested data with a few clusters (Korea)

MLM

Oct 12, 2023

Using robust standard errors for the analysis of binary outcomes with a small number of clusters

CR2 plug in for SPSS can be downloaded from: https://github.com/flh3/CR2

Jan 1, 2023

Using cluster-robust standard errors when analyzing group-randomized trials with few clusters

The SPSS version can be accessed here: https://github.com/flh3/CR2/tree/master/SPSS

Jan 1, 2022