@article{171491,
  author = {Justin Grimmer and Dean Knox and Brandon M. Stewart},
  title = {Na{\"\i}ve regression requires weaker assumptions than factor models to adjust for multiple cause confounding},
  abstract = {<p>The empirical practice of using factor models to adjust for shared, unobserved confounders,\&nbsp;Z, in observational settings with multiple treatments,\&nbsp;A, is widespread in fields including genetics, networks, medicine, and politics. Wang and Blei (2019, WB) formalizes these procedures and develops the "deconfounder," a causal inference method using factor models of\&nbsp;A\&nbsp;to estimate "substitute confounders,"\&nbsp;Ẑ\&nbsp;, then estimating treatment effects by regressing the outcome,\&nbsp;Y, on part of\&nbsp;A\&nbsp;while adjusting for\&nbsp;Ẑ\&nbsp;. WB claim the deconfounder is unbiased when there are no single-cause confounders and\&nbsp;Ẑ\&nbsp;\&nbsp;is "pinpointed." We clarify pinpointing requires each confounder to affect infinitely many treatments. We prove under these assumptions, a na{\"\i}ve semiparametric regression of\&nbsp;Y\&nbsp;on\&nbsp;A\&nbsp;is asymptotically unbiased. Deconfounder variants nesting this regression are therefore also asymptotically unbiased, but variants using\&nbsp;Ẑ\&nbsp;\&nbsp;and subsets of causes require further untestable assumptions. We replicate every deconfounder analysis with available data and find it fails to consistently outperform na{\"\i}ve regression. In practice, the deconfounder produces implausible estimates in WB{\textquoteright}s case study to movie earnings: estimates suggest comic author Stan Lee{\textquoteright}s cameo appearances causally contributed\&nbsp;$15.5 billion, most of Marvel movie revenue. We conclude neither approach is a viable substitute for careful research design in real-world applications.</p>
},
  year = {2023},
  journal = {Journal of Machine Learning Research},
  volume = {24},
  pages = {1-70},
  month = {08/2023},
  url = {https://www.jmlr.org/papers/v24/21-0515.html},
  language = {eng},
}