Bayesian infinite interactive fixed effects modeling for causal inference

Causal inference for single treatment effect estimation is challenging due to the absence of valid control units. The synthetic control method (SCM) offers an innovative way of constructing the so-called data-driven control unit. The generalized synthetic control (GSC) method is proposed as a factor model-based extension of SCM. While GSC improves upon SCM, the performance of GSC heavily depends on the choice of the number of latent factors. To account for the uncertainty associated with the number of factors, we propose to employ a Bayesian infinity factor modeling approach. The key idea of our Bayesian infinity factor modeling is to assign a cumulative shrinkage process prior on the factor loadings. In addition, we apply a Gaussian process approach to infer the non-linear treatment effect. The proposed Bayesian framework enables us to make full Bayesian inference about the time-varying treatment effect. The merits of the proposed Bayesian method are demonstrated through simulation studies and real data analysis.

Bayesian infinity factor model

Causal inference

Interactive fixed effects model

Synthetic control method 

International Society for Bayesian Analysis (ISBA)