Monday Symposium in Measurement and Statistics (MSMS)
Department of Human Development and Quantitative Methodology
Fall 2021
Estimating Bias and Sensitivity of Front-Door Models
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The front-door criterion is a heavily underused analytic method to estimate causal effects in the presence of unobserved confounding. One potential reason why this approach has been largely ignored is the strong set of assumptions that need to be invoked. The front-door estimator yields unbiased total effects between a putative cause and an outcome of interest by decomposing a total effect in unbiased component effects. However, this guarantee of unbiasedness rests strictly on a set of assumptions that can be violated in practice. To illuminate these assumptions and the severity of bias due to their violation, we derive exact bias formulas for each possible violation. We further compare the performance of the front-door estimate under violations with the performance of a naive estimator (that simply regresses the outcome on the putative cause). We show that some violations of assumptions lead to simple confounding bias, but also to collider bias, and bias amplification. We derive all biases analytically, but also supplement our analysis with an extensive simulation, in which we compare biases for a very wide range of parameter values. Using the results from our analysis and simulation, we dissect and explain the nature of bias in the front-door estimate. Finally, we present a simple method to conduct sensitivity analyses using phantom variables in structural equation models.
Dr. Felix Thoemmes works on topics of quantitative methods and design for the social sciences. In particular, he is interested in causal inference, both model-based and design-based.