Set‐theoretic Multimethod Research: The Role of Test Corridors and Conjunctions for Case Selection

Abstract

Set‐theoretic multimethod research (SMMR) using Qualitative Comparative Analysis (QCA) formalizes the choice of cases based on a truth table analysis. We make three recommendations for improving SMMR. First, current standards can lead to faulty case selection if causal inference on a conjunction is the goal. Case selection needs to take into account that the non‐members of a conjunction might be empirically diverse and that only selected types of non‐members are ideal for causal inference. Second, we formally show that cases with similar fuzzy‐set memberships in a term and the outcome are the superior choice for process tracing. They minimize the expected membership in the mechanism and make it most difficult to pass a hypothesis test. Third, we propose formulas that comply with all SMMR principles and identify the best pairs of cases for analysis. We illustrate our arguments with a study of the effectiveness of sanctions against authoritarian regimes.

The Identification of Causal Mechanisms in Sustainable Urban Transitions—A Systematic Approach to Case Selection

“…The potential of a multi-method design is that it combines the strengths and compensates for the limitations of the different methods applied [18]; thus, it is increasingly popular to combine QCA with process tracing via SMMR [18,19,21,23,26]. Employing configurational and mechanistic approaches together provides an accurate picture of the investigated reality, allowing the identification of potential causes and selecting cases for further within-case analysis [23,36].…”

“…SMMR involves an in-depth analysis of the specific causal mechanisms that allows examination of the "why"-of combinations of conditions, via QCA, and the "how"-of the causal mechanism, via process tracing of a causal relationship [37]. SMMR is based on the fact that QCA-based inference becomes stronger "if" and "when" withincase evidence is added via process tracing, with the study of selected cases to establish the existence of causal relationships [19,21,36]. After applying QCA, process tracing is conducted on specific cases to: (a) provide evidence of a causal relationship between a combination of conditions and the outcome; and (b) understand how the combination of conditions produces the outcome by tracing the causal mechanism under certain contextual conditions [38,44].…”

“…Process tracing applied to typical cases aims to identify the causal mechanism that links the sufficient term to the outcome [19,20]. A term will be causal if each of its conjuncts produces a difference in the mechanism [21]. To test this approach, we analyzed whether leaving out any of the conjuncts makes the mechanism disappear, through as many withincase analyses of typical cases as conjuncts exist in the conjunction.…”

“…Likewise, the typical case should be a pathway case, which is uniquely covered by one of the solution paths-typical only for one of the sufficient terms [18,19]. Thus, the best available typical case should meet the following criteria: the FC defines the membership of the typical case in the term (FC ≤ CC)-attribution principle; the corridor for the mechanism is a small test corridor; the membership in the sufficient term is high; the case is uniquely covered by the sufficient term [20,21].…”

“…Thus, Set Theoretic Multi-Method Research (SMMR) is consolidated, whereby the analysis of a truth table, with QCA at a cross-case level, is combined with process tracing at a within-case level. Both techniques-QCA and process tracing-are rooted in fuzzy-set theory [18][19][20][21][22].…”