Two-Stage Structural Equation Modeling : Controlling for Omitted and Confounding Variables in Structural Equation Models

When testing hypotheses, problems of omitted variables / confounding variables arise, understood as variables, which determine both, the variable seen as dependent and the variables seen as independent, resulting in spurious correlations among both. Experimental approaches counter this problem by randomization, regression approaches by including as many potential confounding variables as possible. Both approaches have other limitations, notably regarding testing complex models mapping causal mechanisms with several stages, like the theory of planned behavior or the separation of measurement models linking constructs and indicators and conceptual models linking constructs. Structural equation models (SEMs) allow formulating and testing models with explicit measurement models and capturing complex causal processes involving more than one step. But often, they do not allow for controlling potential confounding variables, as SEMs quickly become too complex to be identified. We argue that by regressing the indicators of constructs in a first stage on control variables and then including the residualized variables into the SEM allows to control for any number of confounding variables while at the same time retaining the relative simplicity of SEMs to capture and illustrate relationships among abstract concepts. At the practical level, using the two stage approach allows to include variables like experimental conditions in addition to continuous variables as control variables. The approach is outlined and illustrated using an empirical example