Bayesian, Frequentist, or Both? Model-Robust Regression and the 'Sandwich' Estimator

• Activity Number: 189
• Type: Invited
• Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
• Sponsor: ENAR
• Author(s): Adam A. Szpiro*+ and Kenneth Rice and Thomas Lumley
• Companies: University of Washington and University of Washington and University of Washington
• Keywords: Robust Regression ; Estimating Equations ; Sandwich Estimator ; Bayesian Inference ; Linear Regression

Abstract

In applied analysis, it is often useful to estimate a linear trend in the data even though classical assumptions of linear regression (i.e., homoscedasticity and linear mean) do not hold. In the frequentist setting, estimating equations and the Huber-White sandwich covariance estimator give asymptotically valid inference, provided that sufficient care is taken to specify the target of inference and the covariate sampling frame. We present a new Bayesian approach that leads to uncertainty estimates with the same robustness properties as the sandwich estimator. Our derivation provides a compelling Bayesian justification for using this simple and popular tool, and it also clarifies what is being estimated when the data-generating mechanism is not linear. We demonstrate our approach using a simulation study and health care cost data from the Washington State Basic Health Plan.