Bias and sensitivity analysis for unmeasured confounders in linear structural equation models

In this paper, we consider the extent of the biases that may arise when an unmeasured confounder is omitted from a structural equation model (SEM) and we propose sensitivity analysis techniques to correct for such biases. We give an analysis of which effects in an SEM are, and are not, biased by an unmeasured confounder. It is shown that a single unmeasured confounder will bias not just one, but numerous, effects in an SEM. We present sensitivity analysis techniques to correct for biases in total, direct, and indirect effects when using SEM analyses, and illustrate these techniques with a study of aging and cognitive function.