Embrace•perform•model: Complexity theory, contrarian case analysis, and multiple realities

This essay describes tenets of complexity theory including the precept that within the same set of data X relates to Y positively, negatively, and not at all. A consequence to this first precept is that reporting how X relates positively to Y with and without additional terms in multiple regression models ignores important information available in a data set. Performing contrarian case analysis indicates that cases having low X with high Y and high X with low Y occur even when the relationship between X and Y is positive and the effect size of the relationship is large. Findings from contrarian case analysis support the necessity of modeling multiple realities using complex antecedent configurations. Complex antecedent configurations (i.e., 2 to 7 features per recipe) can show that high X is an indicator of high Y when high X combines with certain additional antecedent conditions (e.g., high A, high B, and low C)-and low X is an indicator of high Y as well when low X combines in other recipes (e.g., high A, low R, and high S), where A, B, C, R, and S are additional antecedent conditions. Thus, modeling multiple realities-configural analysis-is necessary, to learn the configurations of multiple indicators for high Y outcomes and the negation of high Y. For a number of X antecedent conditions, a high X may be necessary for high Y to occur but high X alone is almost never sufficient for a high Y outcome.