A Bayesian Latent-Factor Framework for Causal Decomposition in High-Dimensional Experiments

Randomized experiments with high-dimensional outcomes, such as product-level purchases, biomarker panels, or digital behavioral traces, typically yield aggregate treatment effects but provide limited insights into the underlying pathways through which interventions operate. We propose a Bayesian framework for decomposing treatment effects across latent behavioral dimensions inferred exclusively from pre-treatment data. The approach combines a causal identification strategy with a mixed-membership factor model implemented through Latent Dirichlet Allocation, yielding additive factor-level outcomes that accommodate sparsity, overlapping item–factor relationships, and uncertainty in latent assignments. We derive a causal decomposition that represents factor-level treatment effects as probability-weighted averages of item-level effects, along with an adjustment term capturing the alignment between latent structure and heterogeneous responses. A joint posterior computation scheme integrates latent factor estimation with treatment-effect inference and propagates uncertainty to all causal estimands. Simulation studies demonstrate that the method reliably recovers both latent factor structure and treatment-effect decompositions under realistic sparsity. In an application to a large-scale randomized promotion experiment at a retailer, the framework identifies interpretable latent behavioral factors, isolates the components through which the promotion operates, and reveals heterogeneity obscured by category-based analyses. The proposed method provides a scalable and causally principled approach for analyzing high-dimensional experimental outcomes. This is joint work with Raghuram Iyengar (Wharton) and Young-Hoon Park (Cornell).