Cluster-robust jackknife and bootstrap inference for logistic regression models

2024-06-02

AI Summary

Standard cluster-robust variance estimators (CRVE) in logistic regression yield severely biased inference under small sample sizes or weak clustering. This paper proposes a novel cluster-robust inference framework that jointly implements cluster-level jackknife and linearized wild bootstrap—introducing the first such combination. We develop a computationally efficient, score-based linearized variance estimator, generalizable to generalized linear models (e.g., probit, logit). Unlike conventional CRVE, our approach avoids strong assumptions about within-cluster correlation structure, substantially improving confidence interval coverage and test power. Extensive simulations demonstrate robust performance across diverse clustering configurations—including few clusters, unbalanced cluster sizes, and low intra-cluster correlation. Empirical applications confirm meaningful corrections to inferential conclusions on real-world data. A publicly available Stata command, `logitjack`, implements the method.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Probabilistic Inference

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Improving reliability of cluster-robust inference for logistic regression
• Proposing computationally efficient linearized jackknife and bootstrap methods
• Addressing limitations of common cluster-robust variance estimators

Innovation

• Cluster-jackknife variance matrix estimator
• Linearized wild cluster bootstrap versions
• Empirical scores for computational efficiency