Two-way fixed effects (TWFE) models are increasingly applied in air pollution epidemiology to estimate associations between temporal changes in pollutant concentrations and health outcomes. Despite their growing use, it is not well established how sensitive TWFE estimates are to different choices of fixed effects (FEs) and interactions, nor how researchers should transparently choose a final model among many plausible specifications. The authors address these gaps by proposing a structured approach for model specification and selection.
The primary aim reported was to systematically assess the sensitivity of TWFE models to alternative FE specifications and to propose a comprehensive decision-making framework for selecting a final TWFE model. The authors illustrate the approach using an empirical case study linking weekly exposure and outcome measures at the ZIP Code Tabulation Area (ZCTA) level.
As an illustrative application, the study examined associations between weekly ZCTA-level mean PM2.5 concentrations and weekly respiratory hospitalizations in California over the period 2011–2019. Further granular details on data sources, inclusion criteria, exposure assessment methods, or hospitalization definitions were not reported in the abstract and therefore are not restated here.
To capture plausible spatiotemporal confounding patterns, the investigators specified a comprehensive set of TWFE models. In total, they proposed 52 candidate TWFE models that represented all plausible combinations of spatial and temporal FEs and their interactions for the study context. The multiplicity of candidate specifications was intended to reveal how estimated associations change with different modeling choices.
The authors introduced a three-stage framework to guide transparent selection of a final TWFE model from many plausible candidates. The three stages reported are:
Stage 1: Use of permutation tests to assess features of the model and evidence against null structure under randomization-based checks.
Stage 2: Application of equivalence testing to evaluate whether estimates from alternative specifications are sufficiently similar to a reference or to each other, informing which specifications yield comparable inference.
Stage 3: Consideration of model complexity to favor parsimonious specifications when multiple models pass statistical checks.
These stages were intended to be applied sequentially to narrow the candidate set and identify a final model that balances robustness and parsimony.
The sensitivity analysis revealed substantial variation in estimated associations across models with different combinations of FEs and their interactions, indicating that the choice of FEs can meaningfully influence inference. Applying their three-stage decision-making framework, the authors selected a final model. That final model produced an effect estimate indicating that a 1 μg/m3 increase in weekly mean PM2.5 concentration was associated with a 0.06% increase in weekly respiratory hospitalizations. The 95% confidence interval reported for this estimate was 0.03% to 0.09%. Standard errors for that final estimate were clustered by ZCTA.
The study highlights that FE selection in TWFE models is not a neutral analytic choice: different plausible FE specifications can yield meaningfully different effect estimates. To improve transparency and robustness of inference, the authors recommend adopting systematic approaches to model specification and selection, such as the three-stage framework they proposed, when using TWFE models in air pollution research. Their framework is presented as a practical guide for future studies aiming to report defensible, transparent TWFE-based estimates.
The abstract listed the following keywords: fine particulate matter; model specification; respiratory hospitalization; two-way fixed effects model. The article is reported as a free article in the American Journal of Epidemiology (2026), with PMID 41885476 and DOI 10.1093/aje/kwag069. Additional methodological or data details beyond those summarized in the abstract were not reported in the source document provided.