Unobserved heterogeneity is common in managerial data and may reflect latent subgroups characterized by different data-generating mechanism. Such heterogeneity is difficult to identify because subgroup assignment is unobserved and subgroup-specific mechanisms may involve not only coefficients but also model specification. To address this challenge, we propose Heterogeneity-aware Symbolic Regression (HSR), an automated estimation framework that jointly identifies latent subgroups and subgroup-specific explicit functions. HSR embeds symbolic regression into a mixture-of-experts structure under generalized Expectation Maximization, forming an estimation core that integrates latent subgroup representation, subgroup-specific explicit function identification, and assignment–function joint updating. HSR accommodates heterogeneity ranging from coefficient variation within a common model family to subgroup-specific function forms identified adaptively from the data. Across synthetic settings, HSR provides accurate latent subgroup assignment, competitive predictive performance, and high accuracy in coefficient and function form identification. Across three empirical case studies spanning individual-level purchase behavior, organization-level workforce turnover, and facility-level environmental risk, HSR reveals model specification heterogeneity in how pre-purchase behaviors relate to purchase price, workforce conditions relate to turnover pressure, and facility and organizational conditions relate to environmental risk. These results show that HSR can identify interpretable subgroup-specific functions that provide a basis for interpretation and decision-relevant analysis.
Yan et al. (Tue,) studied this question.