Cluster-robust jackknife and bootstrap inference for logistic regression models

Abstract: We study cluster-robust inference for logistic regression (logit) models. Inference based on the most commonly-used cluster-robust variance matrix estimator (CRVE) can be very unreliable. We study several alternatives. Conceptually the simplest of these, but also the most computationally demanding, involves jackknifing at the cluster level. We also propose a linearized version of the cluster-jackknife variance matrix estimator as well as linearized versions of the wild cluster bootstrap. The linearizations are based on empirical scores and are computationally efficient. Our results can readily be generalized to other binary response models. We also discuss a new Stata software package called logitjack which implements these procedures. Simulation results strongly favor the new methods, and two empirical examples suggest that it can be important to use them in practice.