Why Standard QCA solutions are valid and true to cases

What is it about?

Can one rely on Standard QCA solutions? and which is better: the parsimonious, or the intermediate? To respond to these questions independently on the parameters of fit, the article considers in QCA a condition has explanatory power if it can order the cases at hand into homogeneous partitions, and develops two indexes that gauge the explanatory power of single conditions alone, and within the starting model.

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Why is it important?

Parsimonious solutions have long been deemed untrue to cases because they can make some necessary condition disappear, which led to the introduction of intermediate solutions. However, intermediate solutions have been deemed invalid because they add conditions that violate the formal criterion of solutions' minimality. This work restores homogeneity as the basic criterion of validity. It clarifies the Standard parsimonious solutions find those 'essential' conditions without which the partitions would become heterogeneous, whereas the Standard intermediate add those further conditions that are implied by the parsimonious. These additions may be 'inessential' yet entertain a set relationship with the parsimonious prime implicants which preserves homogeneity and can be understood as of causal dependence. The bottom line is, as a rule of thumb, if you run a Standard fsQCA and the intermediate solutions improve the fitting of the cases to the shape of sufficiency, you have no reasons to narrow on the parsimonious instead. Of course, provided you have a truth table without contradictory rows, and an interpretable starting model to begin with.