QUALITATIVE COMPARATIVE ANALYSIS VIS-A-VIS REGRESSION
19
missing variables has failed for each combination. In effect, the assumptions about missing
variables employed in each of the multiple iterations of the test are logically incompatible
with each other.
We thus conclude that QCA, in both its Boolean algebraic form and its more re-
cent fuzzy set version, requires extremely restrictive assumptions about missing variables.
Boolean algebraic QCA is only appropriate in contexts where the researcher is certain that
no variables are missing–which, in practice, will typically require elaborate specifications
of numerous, largely uninteresting independent variables. The tests of sufficiency behind
fuzzy-set QCA are applicable when researchers are confident in advance that only one causal
conjunction is relevant–and that all other variation can be treated as completely unsystem-
atic. If such contexts are rare in the social sciences, then QCA techniques are perhaps not
terribly practical.
In fact, regression analysis was originally developed as a way of making inferences in
the presence of specific kinds of omitted variables that are uncorrelated with the included
variables.
8
In particular, the error term in a standard regression analysis is designed to cap-
ture the effects of relevant independent variables that were omitted from the analysis. For
regression to succeed, these omitted variables must meet quite specific conditions. Most
importantly, they must be uncorrelated with the included independent variables. Thus,
ordinary regression fails whenever omitted variables are correlated with the included vari-
ables, but it can succeed if omitted variables are uncorrelated with included variables. By
contrast, QCA always fails when there are omitted variables of any sort. In this sense, QCA
represents a step backwards from regression analysis: it fails to address the very problem
that regression was invented to resolve.
Can We Extend fs/QCA to Fix the Missing Variables Problem?.
A first step in coming to grips with the problem of missing variables in QCA is to
ask, can existing QCA techniques be extended to make these assumptions less restrictive?
8
The specific category of omitted variables of initial concern had to do with measurement error in the
dependent variable. See (Stigler, 1986).
Convention