r-squared or equivalent for QCA

[Sarah Wang]

Hi everyone, 

Could I please get some input into my reply to "r-squared in QCA"?  

I recently received one feedback: "Is there an r-squared or equivalent for QCA? Can we say with any certainty how much of the variance in achievement that these clusters explain?" 

(in the project, the outcome was the high national achievement; 21 cases in the set of high national achievement; the word "clusters" mentioned in the question refer to sufficient components, hence about sufficient solution)

Based on my understanding, my reply is: 

Although there is no concept of variance in QCA due to the fundamental differences between QCA and correlation-based analysis, covU may have some similarities as r- squared. In QCA, covU is unique coverage, suggesting the percentage of all cases’ set membership in the outcome is uniquely covered by single sufficient components. I need to emphasize that 

(1) covU is related to the sufficient component (combinations of conditions), not single conditions (independent variables). 

(2)covU is to explain the cases' set membership in high national achievement. For example, if covU is 0.2 for component 2, it means 20% of all 21 cases’ set membership in the high maths performance is only explained by component 2. 

(3) So covU does not indicate the proportion of the "variance" of the sufficient component in the outcome (dependent variable). (because the outcome had been calibrated into set memebership before the sufficient analysis)

Could you please let me know if there is anything off-track on my understanding in this? Anything that I have missed? 

Thank you all

Kind regards

Sarah 

[Ingo Rohlfing]

It is correct that QCA is not about captured or "explained" variance. Since R-square is a model parameter, the equivalent in QCA is solution coverage. It is the share of the total case membership in the outcome that is covered by the cases total membership in the solution (set membership values and number of cases most likely do not coincide when one works with fuzzy sets). In my understanding, covS is the equivalent of the effect size in a bivariate statistical analysis and represents the cases' total membership in the outcome that is covered by their total membership in the prime implicant at hand. As you say, covU is the coverage of a prime implicant net of the coverage that the cases have in other prime implicants.

Regards

Ingo