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The empirical practice of using factor models to adjust for shared,unobserved confounders, $\mathbf{Z}$, in observational settings with multipletreatments, $\mathbf{A}$, is widespread in fields including genetics, networks,medicine, and politics. Wang and Blei (2019, WB) formalizes these proceduresand develops the "deconfounder," a causal inference method using factor modelsof $\mathbf{A}$ to estimate "substitute confounders," $\hat{\mathbf{Z}}$, thenestimating treatment effects by regressing the outcome, $\mathbf{Y}$, on partof $\mathbf{A}$ while adjusting for $\hat{\mathbf{Z}}$. WB claim thedeconfounder is unbiased when there are no single-cause confounders and$\hat{\mathbf{Z}}$ is "pinpointed." We clarify pinpointing requires eachconfounder to affect infinitely many treatments. We prove under theseassumptions, a na\"ive semiparametric regression of $\mathbf{Y}$ on$\mathbf{A}$ is asymptotically unbiased. Deconfounder variants nesting thisregression are therefore also asymptotically unbiased, but variants using$\hat{\mathbf{Z}}$ and subsets of causes require further untestableassumptions. We replicate every deconfounder analysis with available data andfind it fails to consistently outperform na\"ive regression. In practice, thedeconfounder produces implausible estimates in WB's case study to movieearnings: estimates suggest comic author Stan Lee's cameo appearances causallycontributed \$15.5 billion, most of Marvel movie revenue. We conclude neitherapproach is a viable substitute for careful research design in real-worldapplications.

Na\"ive regression requires weaker assumptions than factor models to adjust for multiple cause confounding