Set-Relational Fit and the Formulation of Transformational Rules in fsQCA

Interest in the application of fuzzy set Qualitative Comparative Analysis (fsQCA) has increased markedly among political scientists in recent years. Although fsQCA is often contrasted with regression analysis, questions of functional form have thus far been hardly addressed. However, functional form matters as much in the former tool kit of social enquiry as it does in the latter. This article demonstrates how coverage as a measure of set-relational fit can guide the formulation of transformational rules similar to the use of the coefficient of determination in regression-analytic tests of functional misspecification. Interaction effects between membership function and crossover anchor choice on coverage are analyzed in the context of set-theoretic relations of sufficiency between condition and outcome. Depending on the relative location of the crossover anchor, changes in the transformational rules by which base variables are calibrated can increase or decrease coverage similar to the effect of changes in functional specification on the coefficient of determination. Most importantly, significant reductions in uncovered membership relative to total membership provide an explicit and transparent foundation on which calibration strategies can be based.