A Bayes Factor for Bounding the Treatment Effect to Address Hidden Bias in Linear Regression
12 Pages Posted: 1 Mar 2018 Last revised: 10 Mar 2018
Date Written: March 7, 2018
A sensitivity analysis in regression aims to find the values of a missing covariate’s hidden bias parameter(s) that would alter the conclusion of the treatment effect estimate that is based on observed adjustment covariates. However, often in practice there is little intuition about the plausible range of hidden bias parameters. A Bayes factor is introduced for the normal linear model, which measures how much the data have changed the odds for some specified hidden bias, versus zero hidden bias. Then a bound for the treatment effect estimate can be determined, based on values of the hidden bias parameter which attain a minimum Bayes factor (e.g., .05). Also, a pseudo-Bayes factor is introduced, which allows for heteroscedasticity. The Bayes factor approach to bounding the treatment effect is illustrated on real data. Related software code is provided as Supplemental Material (available upon request of the author).
Keywords: Causal Inference; Sensitivity Analysis; Bayesian Analysis; Heteroscedastic consistent; Dirichlet process
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