Dear S.R Nikhashemi,

fs/QCA 2.5/3.0 often spits out "ERROR (Quine-McCluskey): The 1 Matrix is Empty" or "ERROR(Quine-McCluskey): The 1 Matrix Contains All Configurations".

The first error message is returned when all your output values are negative, i.e. when there is not a single row in the truth table which is accepted as being sufficient for the outcome. This happens when your consistency cut-off is higher than the consistency score of the best-performing row.

The seond error message is the opposite. It is returned when all your output values are positive, i.e. when there is not a single row in the truth table which is accepted as not being sufficient for the outcome. This happens when your consistency cut-off is lower than the consistency score of the worst-performing row.

Neither case is good, of course. For QCA to work, you need at least one row that is negative and one row that is positive.

However, you will also notice that even though all of your rows are positive / negative, fs/QCA will still produce complex and intermediate solutions. This is only possible because, for producing these two solution types, fs/QCA adds artifical data to your data set through an algorithmic back door (if you want to know more about this process, let me know, it would lead too far here). In other words, these two solution types enlarge your data set without you noticing, and with some quite desastrous consequences (it can be shown that both solution types not only produce inferences beyond your data, but that these inferences often lead you way off path).

I hope this helps.

Best wishes,

Alrik

hi

It is a terminological overlap: in your field (engineering) QCA means Quantum-dot cellular automata, whereas in my field (sociology) QCA means Qualitative Comparative Analysis.

My package QCA will certainly not help you.

Dear Mojtaba,

Thanks

thanks for this Alrik. You are so very right (perhaps, looks you are very often right :) ): by increasing the consistency cutoff the error disappears. I would really be grateful if you could help with a dilemma pervading me now: what will be the most appropriate choice in this case among the followings:

1) just increase the consistency cutoff (I wonder how would you justify this in discussing the analysis)

2) remove from the causal combination object of analysis one factor which represents a necessary factor (if I am not wrong, this is often the practice, actually I seem to remember that fsQCA should remove necessary conditions automatically from the solutions)

I get very different solutions by following the two possible choices above described. Thanks a lot in any case Alrik, your knowledge of the method is deep and the time you take to help others in increasing their understanding of the method, admirable!

Dear Carmine,

Many thanks for your positive words. I simply do what I can to improve QCA-based research (if you want, you can "recommend" the answer above; that will help others who have the same problem find it more easily).

Regarding your questions: You should have no difficulty justifying a higher consistency cut-off, as long as your overall coverage figures do not drop too much at the same time as a result of that decision (consistency and coverage are simply two sides of the same coin, and thus often work against each other in empirical research).

The analysis of necessary conditions and more "advanced" procedures that built on the logic of testing for necessary conditions such as Schneider and Wagemann's T/ESA are not meaningful. In fact, such procedures often distort the analysis up to the point where they induce fallacious inferences.

The reason is that QCA is a method whose purpose is to identify INUS causes and their complex interplay. To this end, a programme's algorithm (Quine-McCluskey in the case of the fs/QCA software) searches for minimally necessary disjunctions of minimally sufficient conjunctions. The mere necessity of a condition, however, is not enough to classify it as an INUS condition. Thus, the algorithm will automatically remove any condition that cannot be shown to be an INUS condition, irrespective of whether it is also a necessary condition because mere necessity has nothing to do with causality. What you should thus never do is to tinker with the minimization protocol, and add to or remove conditions from a final solution only because these conditions are necessary. If you want to read more on this problem, I would recommend the following publications:

• Thiem, Alrik, and Michael Baumgartner. 2016. "Back to Square One: A Reply to Munck, Paine, and Schneider." Comparative Political Studies 49 (6):801-6.
• Thiem, Alrik. 2018. "The Logic and Methodology of “Necessary but Not Sufficient Causality”: A Comment on Necessary Condition Analysis (NCA)." Sociological Methods & Research. Advance online publication. DOI: 10.1177/0049124118782548.

These publications show that the concept of "necessity" is highly overinflated in much of the QCA literature and that many researchers confuse "necessary condition" with "necessary cause".

• Thiem, Alrik. 2017. "Conducting Configurational Comparative Research with Qualitative Comparative Analysis: A Hands-On Tutorial for Applied Evaluation Scholars and Practitioners." American Journal of Evaluation 38 (3):420-33.
• Thiem, Alrik. 2018. "Improving the use of qualitative comparative analysis for inferring complex causation in development and planning research." Journal of Water, Sanitation and Hygiene for Development 8 (4):622-31.

In these publications, I show what will go wrong in empirical research when distorting QCA's minimization protocol by fiddling around with necessary conditions (particularly pp. 625-626 in Thiem (2018) and pp. 427-428 in Thiem (2017)).

I hope this helps. If you have further questions, do not hesitate to ask. I wish you all the best for your QCA research!

Best wishes,

Alrik

Mr Thiem it would be very helpful if you could provide to me more information about this algorithmic back door you mentioned before.

Thank you in advance

Dear Anastasios,

Many thanks for your question. A detailed explanation will be provided in my forthcoming article (Sociological Methods & Research) "Beyond the Facts: Limited empirical diversity and causal inference in Qualitative Comparative Analysis".

But the essence of the argument is as follows: Conservative/complex solutions in QCA (QCA-CS) are not based on empirical data only, as most QCA textbooks tell you (e.g., Schneider & Wagemann, 2012: 162), but on your empirical data + a set of artificial data that are added "through the back door". "Back door" because it is not obvious to the user which data these are before having run the analysis: for conservative solutions, it's all so-called "simplifying assumptions" (which you don't know until after you've run the analysis), for intermediate solutions (QCA-IS), it's all so-called "difficult counterfactuals" (same here).

In the article, I use a classical example from Ragin (1987: 105-6; slightly adapted in lay-out):

A | B | C | OUT(F) | Cases

0 | 0 | 0 | 0 | a

0 | 0 | 1 | 1 | b

0 | 1 | 0 | 0 | c

0 | 1 | 1 | 1 | d

1 | 0 | 0 | 0 | e

1 | 0 | 1 | 1 | f

1 | 1 | 0 | ? | -

1 | 1 | 1 | ? | -

According to Ragin (1987, 105), "[a] conservative statement of what the truth table shows [...] is F = aC + bC", or expressed in logic notation, aC v bC F (lower-case letters stand for ...{0} and upper-case for ...{1}; i.e. A means A{1}, a means A{0}).

Given the declared goal of QCA to identify INUS conditions and their respective interplay (http://eprints.ncrm.ac.uk/250/1/What_is_QCA.pdf; oddly enough, I've seen some people in the "QCA community" claiming that QCA has nothing to do with INUS conditions), QCA-CS thus makes the following set of causal claims 1 to 5:

Now, if you know what INUS conditions are, you know that these are all conditions X for which it is true that some XQ -> Z, while it is false that xQ -> Z.

Let's apply this rule to claim 1 first. Clearly, claim 1 is warranted because the pair of cases [b,a] from the table above show that abC -> F is true, while abc -> F is false. And actually, we have two other pairs of cases that provide evidence for claim 1, namely pair [d,c] and pair [f,e]. So there's definitely evidence for the causal relevance of C.

What about a? As it turns out, a cannot be shown to be an INUS condition, and thus it cannot be shown to be causally relevant to F. Why? The only cases where a appears and F is present are case b (abC) and case d (aBC). The problem: For case b, we have no matching case which shows that AbC -> F is false (AbC is instantiated by case f, for which AbC -> F is true), and for case d, we have no matching case which shows that ABC -> F is false. But this time, ABC is a so-called "remainder" in QCA-speak.

In other words, for QCA-CS to declare a to be an INUS condition, it must put a "0" into the OUT(F) column for row ABC. But what does putting a "0" there mean? It means that QCA-CS declares the sufficiency statement ABC -> F to be false. Yet, any sufficiency is only false if the antecent is true and the consequent false (check any intro-book on Boolean algebra). Put differently, QCA-CS creates an artifical case that instantiates ABC and f.

In summary, both conservative and intermediate solutions create artifical data, which the parsimonious solution does not. In fact, the parsimonious solution also does not create untenable simplifying assumptions or anything of that kind. If you want to carry out evidence-based empirical data analysis with QCA, you need the parsimonious solution. If you want to do non-evidence-based fabricated data analysis with a high risk of committing causal fallacies, the conservative and intermediate solutions work very well (see also Baumgartner and Thiem 2017).

I hope this explanation helps a little. If you have any further questions, please don't hesitate to ask.

Best wishes,

Alrik

References

• Baumgartner, Michael, and Alrik Thiem. 2017. "Often Trusted but Never (Properly) Tested: Evaluating Qualitative Comparative Analysis." Sociological Methods & Research. Advance online publication. DOI: 10.1177/0049124117701487.
• Ragin, Charles C. 1987. The Comparative Method: Moving beyond Qualitative and Quantitative Strategies. Berkeley: University of California Press.
• Schneider, Carsten Q., and Claudius Wagemann. 2012. Set-Theoretic Methods for the Social Sciences: A Guide to Qualitative Comparative Analysis (QCA). Cambridge: Cambridge University Press.

Thank you very much for you detailed response mr Alrik. It is very helpful, like your whole research about QCA.

Best regards,

Tasos