Missing data

Pooling clubSandwich results across multiple imputations

A colleague recently asked me about how to apply cluster-robust hypothesis tests and confidence intervals, as calculated with the clubSandwich package, when dealing with multiply imputed datasets. Standard methods (i.e., Rubin’s rules) for pooling estimates from multiple imputed datasets are developed under the assumption that the full-data estimates are approximately normally distributed. However, this might not be reasonable when working with test statistics based on cluster-robust variance estimators, which can be imprecise when the number of clusters is small or the design matrix of predictors is unbalanced in certain ways.