Targeted After Generative (TAG) Learning for Causal Inference with Latent Variables

Habarurema, Jean-Baptiste; Kelcey, Ben; Ataneka, Amota

Latent variables and causal inference are central to implementing empirical research and advancing substantive theory across the social sciences. Conventional latent variable frameworks such as structural equation modeling (SEM) are constrained by several simplifying assumptions (e.g., linearity, additivity, correct model specification). In this study, we relax key SEM assumptions by building data adaptive estimation methods for causal inference with latent variables. We developed a theory-driven Targeted After Generative (TAG) learning framework that integrates SEM-informed variational autoencoders (SEM VAEs) with targeted machine learning to estimate the average treatment effect. On the generative side, the SEM VAE encodes theory aligned neural networks that learn latent variable distributions through flexible joint modeling of measurement and structural parameters. On the targeted learning side, we construct an efficient influence function for the treatment effect with the SEM-VAE implied posterior distribution of the latent variables to estimate the average effect. Across simulations, the TAG learning approach outperforms alternative approaches and demonstrates low to no bias even in adverse conditions. TAG learning offers a theory-driven flexible approach with methodological promise for causally interpretable data-adaptive analysis with latent variables. More practically, the framework allows estimation of causal effects involving latent variables even in the presence of unknown functional relationships in the measurement and structural models (e.g., data adaptive effect estimation for nonlinear/nonadditive SEMs).

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