Measuring Model Misspecification: Application to Propensity Score Methods with Complex Survey Data.

Area of Science:

• Statistics
• Causal Inference
• Econometrics

Background:

• Parametric models are susceptible to misspecification, potentially compromising causal inference.
• Formal measures and consequences of model misspecification in causal inference are underdeveloped.
• Propensity score methods are widely used but sensitive to model assumptions.

Purpose of the Study:

• To propose a metric for quantifying model misspecification in causal inference.
• To investigate the impact of model misspecification on common causal inference estimators.
• To assess the sensitivity of different estimators to outcome and treatment assignment model misspecification.

Main Methods:

• Developed a novel measure for model misspecification.
• Evaluated three propensity score-based estimators: full matching, nearest neighbor matching, and weighting.
• Assessed estimator performance under simple random sampling and complex survey designs.

Main Results:

• Increasing misspecification in propensity score or outcome models directly increases bias and root mean square error.
• Higher misspecification leads to decreased confidence interval coverage for treatment effect estimates.
• Findings were consistent across simple random sampling and complex survey designs.

Conclusions:

• Model misspecification poses a significant threat to the validity of causal inference.
• Propensity score-based estimators exhibit varying degrees of sensitivity to misspecification.
• Robustness checks across sampling designs confirm the detrimental effects of model misspecification.