Joint Deep Learning for Covariate Decomposition and Treatment Effect Estimation

Abstract

This study proposes a joint deep learning method, namely, confounding factor joint decomposition under counterfactual regression (CFJD-CFR), to identify a minimum adjustment covariate set and estimate the average treatment effect (ATE). CFJD-CFR includes two levels: feature learning and prediction model. Feature learning constructs the objective function based on clear variable attribute recognition criteria to identify and decompose a covariate set of different attributes into four disjoint sets of factors: instrumental, confounding, predicting, and noise variables. The output of feature learning is then introduced into the prediction model as its input to build a joint deep learning model and reduce the systematic errors caused by step-by-step learning. The proposed method combines deep representation learning, feature selection, and prediction under the structural equation modeling framework. Simulation studies show that CFJD-CFR can effectively identify the minimum adjustment covariate set and consistently outperform other methods for ATE estimation. The proposed method is applied to the Chinese General Social Survey study. New insights into the difference in social welfare policy preference between urban and rural residents in China are obtained.

Keywords:

• Average treatment effect
• counterfactual framework
• covariate decomposition
• factor analysis
• joint deep learning

Additional information

Funding

This research was supported by GRF grant 14302519 from the Research Grant Council of the Hong Kong Special Administration Region, the State’s Key Social Science Research Project from the National Office for Philosophy and Social Science (21ATJ005), and the Fundamental Research Funds for the Central Universities from Zhongnan University of Economics and Law (112/31512211201).