What’s Missing From the Model? Automating the Search for Omitted Confounders

In the social and behavioral sciences, structural equation modeling (SEM) is a commonly used approach to test hypothesized relationships among observed and unobserved (latent) variables. Yet even well-specified models may omit variables that could influence the relationships being studied, potentially affecting the conclusions drawn from the analysis. In a recent article published in Structural Equation Modeling: A Multidisciplinary Journal, UMN Psychology faculty Katerina Marcoulides and collaborators highlight the importance of sensitivity analysis for evaluating how the results may be affected by omitted confounders. . However, existing approaches generally require researchers to specify in advance how a potential omitted confounder may relate to the variables in the model, a task that becomes increasingly difficult as the model complexity increases.  To address this challenge,  Marcoulides and colleagues have introduced an automated sensitivity analysis framework for SEM using the Tabu Search (TS) metaheuristic optimization algorithm.

In the article, entitled “Sensitivity Analyses for Omitted Confounders in Structural Equation Models with Tabu Search Optimization,” Marcoulides and colleagues describe how the TS framework works. First, TS includes a neighborhood search where the algorithm begins with a possible solution and makes incremental changes to the sensitivity parameters, checking nearby solutions (i.e., its neighborhood) to see if they work better in the model. Second, it includes a Tabu list, which is a list of models already examined to ensure continued forward progress. Finally, TS automates the search for solutions that meet the specified optimization criteria, eliminating the need to a priori specify and manually examine different combinations of sensitivity parameters.

To demonstrate how the TS algorithm can be used to conduct a sensitivity analysis, Marcoulides and colleagues examined a study from 2015 that looked at the emotional and behavioral problems of children in foster care, adding a phantom variable (i.e., an unmeasured confounder) to the original model. Using the TS optimization algorithm, results showed that three path coefficients in the model changed in statistical significance. However, the sensitivity parameters required to flip these path significances were noticeably larger than the standardized coefficients in the original model. Therefore, an omitted confounder would need to have a particularly strong relationship across the variables to alter the study’s conclusions. These findings provide evidence that the original study’s conclusions were robust to potential omitted confounders.

Marcoulides and colleagues demonstrate how the Tabu Search (TS) metaheuristic optimization algorithm can provide a systematic and automated approach for evaluating the sensitivity of SEM results to potential omitted confounders. By identifying the conditions under which model estimates or conclusions may change, the approach can help researchers more rigorously evaluate the robustness of their conclusions and identify potential areas for model improvement or future research.