Grouped fixed effects regularization for binary choice models

2025-02-10

AI Summary

This paper addresses three key challenges in binary panel data models: biased estimation of average partial effects, invalid statistical inference, and the inability to predict outcomes for units with no within-unit variation—problems arising from complete separation. To resolve these issues, we propose a grouped fixed-effects regularization approach. Innovatively, we employ k-means clustering to discretize unobserved heterogeneity and replace conventional within-unit variation with within-group response variation, thereby mitigating complete separation while controlling parameter proliferation. Guided by asymptotic theory, we develop an optimal group-number selection criterion, yielding a unified estimation framework applicable to both panel logit and probit models. Monte Carlo simulations demonstrate that our method eliminates estimation bias and restores valid inference. Empirically, it substantially expands predictive coverage—enabling, for the first time, coherent predictions for numerous units exhibiting invariant responses across time.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Graphical Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We study the application of the grouped fixed effects approach to binary choice models for panel data in presence of severe complete separation. Through data loss, complete separation may lead to biased estimates of Average Partial Effects and imprecise inference. Moreover, forecasts are not available for units without variability in the response configuration. The grouped fixed effects approach discretizes unobserved heterogeneity via k-means clustering, thus reducing the number of fixed effects to estimate. This regularization reduces complete separation, since it relies on within-cluster rather than within-subject response transitions. Drawing from asymptotic theory for the APEs, we propose choosing a number of groups such that clustering delivers a good approximation of the latent trait while keeping the incidental parameters problem under control. The simulation results show that the proposed approach delivers unbiased estimates and reliable inference for the APEs. Two empirical applications illustrate the sensitivity of the results to the choice of the number of groups and how nontrivial forecasts for a much larger number of units can be obtained.

Problem

• Addresses complete separation bias in binary choice panel data models
• Reduces incidental parameters via k-means clustering of fixed effects
• Enables forecasting for units without response variability through regularization

Innovation

• Grouped fixed effects discretize heterogeneity via clustering
• Reduces complete separation using within-cluster transitions
• Selects optimal group count balancing approximation and bias