Multiple Heckman Selection Model

2026-05-03

AI Summary

This study addresses the challenge of modeling multivariate outcomes in matrix-valued data affected by sample selection bias. It proposes the first extension of the Heckman selection model to matrix-variate settings by introducing a framework based on the matrix normal distribution. The method explicitly captures dependence structures across both rows and columns and effectively corrects for selection bias through parameter estimation via an ECM algorithm. Furthermore, it establishes a theoretical connection to the multivariate unified skew-normal (SUN) distribution, enabling closed-form parameter updates. The efficacy and practical utility of the approach are demonstrated through comprehensive simulations and analyses of two real-world datasets. An implementation of the proposed method is publicly available in the R package mvHeckman.

Abstract

We introduce a novel matrix-variate extension of the Heckman selection model to accommodate multiple outcomes, providing a flexible and natural generalization of classical selection models for matrix-valued data. By relying on the matrix normal distribution, the proposed model captures dependencies across both rows and columns while accounting for selection bias. An Expectation/Conditional Maximization (ECM) algorithm is developed, yielding closed-form updates for all model parameters. We investigate key theoretical properties, including the connection between sample selection models and the recently developed multivariate unified skew-normal (SUN) distribution. The performance of the proposed approach is assessed through simulation studies, and its practical utility is illustrated using two real datasets. The proposed method is implemented in the R package mvHeckman.

Problem

• Heckman selection model
• matrix-variate data
• selection bias
• multiple outcomes
• matrix normal distribution

Innovation

• matrix-variate Heckman model
• selection bias
• matrix normal distribution
• ECM algorithm
• unified skew-normal distribution