Naive regression requires weaker assumptions than factor models to adjust for multiple cause confounding

The empirical practice of using factor models to adjust for shared, unobserved confounders, $\boldsymbol{Z}$, in observational settings with multiple treatments, $\boldsymbol{A}$, is widespread in fields including genetics, networks, medicine, and politics. Wang and Blei (2019, WB) generalize these procedures to develop the “deconfounder,” a causal inference method using factor models of $\boldsymbol{A}$ to estimate “substitute confounders,” $\widehat{\boldsymbol{Z}}$, then estimating treatment effects---regressing the outcome, $\boldsymbol{Y}$, on part of $\boldsymbol{A}$ while adjusting for $\widehat{\boldsymbol{Z}}$. WB claim the deconfounder is unbiased when (among …

assumptions causal inference fields genetics inference medicine multiple networks politics practice regression