Identification Requirements for Residual-based Case Selection in Mixed-methods Research

The growing work on causal modeling has produced as one key insight that we should not give a causal interpretation to estimates of controls. We should only interpret the treatment effect of interest. I show that this guidance that is valid for treatment effects is not necessarily valid for case selection in mixed-methods research when cases are selected based on their residuals. The effect of a control variable needed to identify the treatment effect may not itself be identified. While unproblematic for treatment effect interpretation, the resulting bias undermines the role that residuals are supposed to play for case selection. Guided by the distinction between good, bad, and neutral controls, I explain what identification assumptions must be met in mixed-methods research to use residuals for case selection. I present practical guidance on how to perform residual-based case selection in mixed-methods studies.