Why combine PLS-SEM and fsQCA
PLS-SEM estimates the net effect of each construct, assuming that effects add up and that one model fits everyone. Fuzzy-set qualitative comparative analysis (fsQCA) drops that assumption. It looks for configurations, combinations of conditions that are consistently linked to the outcome, and it allows several different configurations to lead to the same result (equifinality).
Using the PLS-SEM latent variable scores as the input to fsQCA is now an established design in management, marketing, tourism and information systems research (Rasoolimanesh et al., 2021). The scores are already reliable, validated measures of each construct, so the configurational analysis starts on solid ground.
In PLS-SEM Studio, run the PLS-SEM analysis first and open the fsQCA step. The scores are already there.
Step 1: Calibrate the sets
fsQCA works with membership scores between 0 and 1, so each construct score is calibrated into a fuzzy set. The direct method (Ragin, 2008) needs three anchors:
- Full membership, mapped to 0.95;
- The crossover point, mapped to 0.50, where a case is neither in nor out of the set;
- Full non-membership, mapped to 0.05.
For latent variable scores, percentile anchors of 95, 50 and 5 are common (Pappas and Woodside, 2021). If you rescale the scores to the original response scale, theory-based anchors such as 6, 4 and 2 on a 7-point scale are also defensible. Because a case with a membership of exactly 0.50 cannot be assigned to a truth-table row, add 0.001 to such values, as Fiss (2011) suggests; the app does this when the option is ticked.
Step 2: Test necessary conditions
A condition is necessary when the outcome cannot occur without it. Check each condition and its negation (~X) before the sufficiency analysis.
| Measure | Meaning | Guideline |
|---|---|---|
| Consistency | How far the outcome is a subset of the condition | ≥ 0.90 suggests necessity |
| Coverage | How relevant the condition is to the outcome | Higher is more relevant |
| Relevance of necessity (RoN) | Whether the condition is trivially present in almost every case | Low values signal a trivial condition |
Step 3: Build the truth table
With k conditions there are 2k possible combinations. Each case belongs to the one row where its membership is above 0.5. For each row the app reports the number of cases, the raw consistency (how reliably the configuration leads to the outcome) and the PRI consistency (which penalises configurations that are also subsets of the outcome's absence).
Two thresholds decide which rows count as sufficient:
- Frequency threshold. Rows with fewer cases are treated as logical remainders. Use 1 or 2 for small samples and a higher value for large samples, keeping at least 75–80% of cases in the analysis.
- Consistency threshold. At least 0.80 is standard; many studies also require PRI of at least 0.70 or 0.75.
Step 4: Read the three solutions
The sufficient rows are simplified with Boolean minimisation (the Quine–McCluskey algorithm):
- The complex solution uses no logical remainders. It is the most detailed and the least simplified.
- The parsimonious solution uses every remainder that simplifies the result. Its conditions are the core conditions.
- The intermediate solution uses only remainders that agree with your directional expectations, such as "high trust contributes to high intention". It is the solution most studies interpret.
For each configuration, report the raw coverage (share of the outcome it explains), the unique coverage (share only it explains) and its consistency, together with the overall solution coverage and consistency. Solution consistency above 0.80 and coverage between 0.25 and 0.90 are usual.
Step 5: Present the configuration chart
Fiss (2011) introduced the chart most journals now expect. Each column is a configuration; each row is a condition.
- A large filled circle (●) marks a core condition that is present: it appears in both the intermediate and parsimonious solutions.
- A small filled circle (•) marks a peripheral condition that is present: only in the intermediate solution.
- A crossed circle (⊗) marks a condition that must be absent, large for core and small for peripheral.
- A blank cell means the condition does not matter in that configuration.
PLS-SEM Studio builds this chart automatically and exports it with the other tables. Run the analysis for the absence of the outcome too: the configurations for "low intention" are often not the mirror image of those for "high intention" (causal asymmetry).
Reporting checklist
- Why you combined PLS-SEM and fsQCA, and that the input is the latent variable scores.
- The calibration anchors for every set, and the 0.5 adjustment if used.
- The necessity table.
- The frequency, consistency and PRI thresholds, and the share of cases retained.
- The configuration chart with raw and unique coverage, consistency and solution measures.
References
- Fiss, P. C. (2011). Building better causal theories: A fuzzy set approach to typologies in organization research. Academy of Management Journal, 54(2), 393–420.
- Pappas, I. O., & Woodside, A. G. (2021). Fuzzy-set qualitative comparative analysis (fsQCA): Guidelines for research practice in information systems and marketing. International Journal of Information Management, 58, 102310.
- Ragin, C. C. (2008). Redesigning social inquiry: Fuzzy sets and beyond. University of Chicago Press.
- Rasoolimanesh, S. M., Ringle, C. M., Sarstedt, M., & Olya, H. (2021). The combined use of symmetric and asymmetric approaches: Partial least squares-structural equation modeling and fuzzy-set qualitative comparative analysis. International Journal of Contemporary Hospitality Management, 33(5), 1571–1592.
- Schneider, C. Q., & Wagemann, C. (2012). Set-theoretic methods for the social sciences. Cambridge University Press.