QuickPLS Must every kind of partner be involved in a circular business?
A business might reuse materials through close supplier relationships. Another might depend on customers returning products. A configuration question asks whether different partner combinations can accompany circular practices. It leaves room for several routes rather than treating every relationship as equally necessary.
Zhu and colleagues studied 127 Baltic small and medium-sized enterprises. Their paper combined structural modelling with fsQCA to examine collaboration, circular practices and performance. This lesson focuses on the supported fsQCA part. It does not reproduce the paper's ordinal DWLS structural estimation, survey measures or empirical solutions.
Use three conditions so every combination can be inspected
The original exercise contains 144 fictional repair and reuse businesses. Each has a continuous 1–7 assessment of supplier collaboration, customer collaboration, collaboration with other organisations and circular operating practices. One row is one business.
Ask which partner combinations accompany strong circular practices. Three conditions produce eight possible truth-table configurations. This is small enough to read each row and its cases, making it a useful exercise in the difference between AND, OR, absence and omission.
These are invented assessments, not latent-variable scores exported from a fitted model. Do not apply reliability statistics to a single summary score or imply that a good configuration validates the underlying assessment instrument. In a real survey, measurement quality would need its own evidence before the scores were used.
On a small screen, swipe the table sideways to see every column.
| Column | Set definition | Role |
|---|---|---|
| SUPPLY | Strong supplier collaboration | Condition |
| CUSTOM | Strong customer collaboration | Condition |
| OTHER | Strong collaboration with other organisations | Condition |
| CIRCULAR | Strong circular operating practices | Outcome |
| case_id | Fictional business identifier | Label |
Step 1. Import the scores and define the crossover
Choose File > Import Data… in a writable project, then Choose data file…. In Review & import, confirm raw data, Header row 1, comma separator, Decimal convention Dot (1.25) and Continuous analytical columns. Choose Import dataset and confirm Dataset imported and verified.
Check that the file has 144 complete cases and that the four scores fall within 1–7. No reverse coding is needed. A low collaboration assessment means little evidence of that relationship; it is not a missing response.
Use 2, 4 and 6 as exclusion, crossover and inclusion under the teaching rubric. At the crossover, a case is neither more in nor more out of the set. Inspect values close to 4 because the distinction between a condition being present or absent in a truth-table configuration depends on which side of the membership crossover the case falls.
The paper's calibration choices are not a universal rule for this file. Percentile anchors describe positions in a particular sample. They do not automatically establish what strong collaboration means. Our exercise instead gives the anchors a declared, invented rubric meaning.
Step 2. Calculate the CIRCULAR baseline in QuickPLS
In Model and data > Case memberships and source rows, locate C0016. Compare SUPPLY and CUSTOM with CIRCULAR and with the matching case table below. Read this business’s memberships before describing what the partnership pathway covers.
Open the fsQCA settings
With the imported dataset selected, choose Calculate…. In Find a method select Fuzzy-set Qualitative Comparative Analysis. Open Method settings. The form starts with Conditions and Outcome and case identity.
Assign the conditions and outcome
Under Conditions choose Add condition for each of SUPPLY, CUSTOM and OTHER, in that order. Under Outcome and case identity select CIRCULAR as Outcome variable, Presence of the outcome as Analyse and case_id as Case identifiers. Check that only the intended conditions appear; the case label is not an analytical condition.
Calibrate every selected column
For each condition and the outcome choose Direct fuzzy-set calibration. Enter exclusion 2, crossover 4 and inclusion 6. Explain the column’s set definition and the invented assessment rubric in its anchor rationale. These increasing anchors make a higher raw score correspond to greater membership. There is no separate inclusion-membership entry in this form.
Set the baseline thresholds
Under Truth table and solution assumptions set Frequency threshold to 2, Consistency threshold to 0.80 and PRI threshold to 0.50. Leave Request intermediate solutions with explicit directional expectations unchecked for this baseline. The reference answer uses the conservative family from the completed output; it is not a family selected in this settings form.
Calculate and check the result
Choose Start calculation and wait for completion. Check the outcome, calibration, thresholds and included-case count in the completed result before interpreting it. The reference includes all 144 cases. If your result differs, inspect Exclusions and the selected settings rather than changing the answer to fit the reference.
Read one complete solution
In Results, select the completed calculation in Result. Under Estimates open Truth table and read frequency, consistency and PRI together. Then open Overall solution fit — every alternative. Use the conservative rows to compare with this lesson’s reference answers; keep the Solution identifier with the family. In Pathway fit and coverage — every alternative, read all pathways belonging to that same family and solution. Do not combine pathways from different complete alternatives. An alternative number identifies an expression; it does not rank its quality.
Check the case memberships
Under Model and data open Case memberships and source rows. Locate C0016 by its case identifier and compare SUPPLY and CUSTOM with CIRCULAR. Use the lesson’s checked case table to follow the membership calculation. One case illustrates the pathway; its membership is not the pathway’s overall consistency.
Step 3. Check the answers for the 144-case file
Use direct logistic calibration for every selected condition and outcome: exclusion 2, crossover 4, inclusion 6; the calibration used by the reference assigns membership 0.95 at the inclusion anchor. The baseline uses frequency 2, row consistency 0.80 and PRI 0.50. Read the conservative rows in the completed solution tables. 144 of 144 cases are included; excluded case identities, if any, are in the download.
For CIRCULAR, 2 truth-table rows are positive, 6 negative and 0 remainders. There are 1 complete conservative alternative(s). Alternative 1 has consistency 0.846, coverage 0.602 and PRI 0.666.
About these answers: Reference answers calculated with R QCA and independently checked. These tables are not outputs from a QuickPLS app run.
On a small screen, swipe the table sideways to see every column.
| Outcome | Selected alternative | Solution consistency | Solution coverage |
|---|---|---|---|
| CIRCULAR | 1 of 1 | 0.846 | 0.602 |
What the separate checks cover
666 numerical comparisons passed tolerance 0.000000000001. Python independently recalculated memberships, case assignments, supported-row consistency and PRI, pathway and solution fit, and checked that each conservative alternative covers exactly the positive Boolean rows. This does not prove that the minimiser found every globally minimum expression and does not execute QuickPLS.
Step 4. Read the complete CIRCULAR alternative
The table gives every pathway in reference alternative 1. Read * as AND, ~ as absence, and the rows together as OR. An omitted condition can be present or absent within that term. Keep the complete expression together. The downloadable calculation files include any other returned alternatives.
The CIRCULAR outcome is a calibrated membership, not a pass/fail prediction. Raw coverages can overlap; adding them does not give solution coverage.
About these answers: Reference answer from R QCA 3.25, with independent checks of calibration, pathways and fit.
On a small screen, swipe the table sideways to see every column.
| Pathway | Consistency | Raw coverage | Unique coverage |
|---|---|---|---|
| SUPPLY* | 0.846 | 0.602 | 0.602 |
Step 5. Follow one actual practice case: C0016
For case C0016, the membership in SUPPLY*CUSTOM is 0.664. Take the smallest membership across the conditions in that term, complementing a membership first when it has ~. The outcome membership is 0.843. This is one case inside a pathway, not the pathway’s overall consistency.
About these answers: Values calculated from this CSV using the stated logistic calibration.
On a small screen, swipe the table sideways to see every column.
| Condition or outcome | Raw score | Calibrated membership |
|---|---|---|
| SUPPLY | 4.4617 | 0.664 |
| CUSTOM | 5.1106 | 0.837 |
| OTHER | 2.9689 | 0.180 |
| CIRCULAR | 5.1431 | 0.843 |
Step 6. Compare the planned threshold changes
The frequency / consistency column lists the rules applied to truth-table rows. The final consistency column measures the minimised solution. These are different quantities; a row threshold of 0.85 does not require solution consistency to exceed 0.85. A frequency increase can remove observed support and create more remainders.
These runs change frequency or row consistency while holding calibration fixed. They do not test other calibration anchors, outcome negation or another solution family. If the lesson asks you to explore those choices, save and report them as additional runs.
About these answers: External reference runs, with every returned conservative alternative retained.
On a small screen, swipe the table sideways to see every column.
| Outcome / change | Frequency / consistency | Positive rows | Alternatives | Solution consistency | Solution coverage |
|---|---|---|---|---|---|
| CIRCULAR: baseline | 2 / 0.80 | 2 | 1 | 0.846 | 0.602 |
| CIRCULAR: frequency | 3 / 0.80 | 2 | 1 | 0.846 | 0.602 |
| CIRCULAR: consistency | 2 / 0.85 | 2 | 1 | 0.846 | 0.602 |
Step 7. Read a missing symbol correctly
Imagine the illustrative expression SUPPLY * CUSTOM + OTHER. It describes either strong supplier and customer collaboration together, or strong collaboration with other organisations. OTHER standing alone is one hypothetical sufficient pathway under the stated analysis; it is not evidence that other relationships never matter.
In the first pathway, OTHER is omitted. Its value is unrestricted by that term. The expression does not require weak collaboration with other organisations. By contrast, SUPPLY * ~CUSTOM explicitly requires low membership in strong customer collaboration.
Negation is also different from a second independent construct. The absence of strong customer collaboration is calculated from that set's membership. It does not measure customer conflict, dissatisfaction or resistance. Those concepts would need their own definitions and evidence.
On a small screen, swipe the table sideways to see every column.
| Notation | Plain reading | Common mistake |
|---|---|---|
| SUPPLY * | Both memberships jointly | Treating the terms as two separate routes |
| SUPPLY + | Either pathway, allowing overlap | Counting a business twice in solution coverage |
| ~CUSTOM | Absence of strong customer collaboration | Calling it customer hostility |
| CUSTOM omitted | No restriction on CUSTOM in that term | Saying customers must be uninvolved |
| Alternative solution | Another complete returned expression | Combining its favourite terms with another alternative |
Calculate conjunction and overlap for one business
Hypothetical example
Illustrative reading example
Suppose a fictional business has SUPPLY membership 0.90, CUSTOM 0.60, OTHER 0.30 and CIRCULAR 0.75. Membership in SUPPLY * CUSTOM is min(0.90, 0.60), or 0.60. Membership in SUPPLY * CUSTOM + OTHER is max(0.60, 0.30), also 0.60.
For this case the proposed solution is contained within the outcome because 0.60 does not exceed 0.75. The case contributes 0.60 to the overlap used in sufficiency consistency. Its outcome membership is not fully covered: the solution membership is lower by 0.15.
Now imagine another case with solution membership 0.85 and outcome membership 0.40. It belongs strongly to the proposed solution but only weakly to the outcome. Such a case weakens consistency and deserves substantive investigation. It should not be removed just because it complicates the expression.
All memberships in this worked example are invented. They explain fuzzy AND as the minimum and fuzzy OR as the maximum. They are not fitted results, expected CSV answers or observations reported in the cited paper.
Step 8. Do not confuse a common partner with a required partner
Inspect necessity before claiming that a particular partner relationship is indispensable. A condition may appear in many pathways simply because it is common in the sample. Read necessity consistency together with relevance and the cases that challenge the proposed relationship.
For an optional low-outcome analysis, reopen the fsQCA settings, keep CIRCULAR as the outcome and set Analyse to Negation of the outcome (separate analysis). Keep the condition definitions, start a new calculation and read its own truth table and solutions. The supplied answer tables concern outcome presence; calculate and report the negated-outcome result separately.
Set a limited sensitivity plan before calculating alternatives: compare consistency 0.80 with 0.85, and separately compare frequency 2 with 3. Inspect the changed rows and cases. If a route disappears only under a stricter threshold, report the dependence instead of describing the original route as universally sufficient.
Use the small truth table to diagnose mistakes
Because there are only eight possible configurations, you can usually trace a surprising result to a small number of rows. This makes the exercise useful for learning the logic. It does not mean that every three-condition study has adequate theoretical coverage.
On a small screen, swipe the table sideways to see every column.
| Symptom | Check | Action |
|---|---|---|
| The report says a partner is absent because its symbol is missing | The pathway notation and legend | Replace absence with unrestricted unless the negated symbol is present. |
| A high consistency route covers little circular practice | Raw and unique coverage | Describe its narrow scope and identify covered businesses. |
| A customer condition is called necessary | The separate necessity results | Check containment and relevance rather than pathway frequency. |
| Several cases sit at the crossover | Raw ratings, calibration and case policy | Make explicit justified decisions; do not nudge memberships automatically. |
| Positive and negative outcomes have different routes | Outcome definitions and actual saved results | Explain asymmetry rather than forcing mirrored expressions. |
| A configuration changes after one coding fix | Which original case and membership changed | Document the correction and rerun the affected saved analyses. |
Step 9. Describe the pathways in language a reader can test
In Results, write each pathway first in symbols and then in ordinary language. Insert the actual consistency, raw coverage and unique coverage from the selected complete solution. Describe one business that illustrates the conjunction and one that challenges it. State whether any conclusion changes under the planned alternatives.
| Pathway or result | What to report |
|---|---|
| Each pathway | Expression and meaning of omitted versus absent conditions |
| Pathway fit | Consistency, raw coverage and unique coverage |
| Whole solution | Family, complete alternative, consistency and coverage |
| Necessity | Separate fit and relevance evidence |
| Outcome absence | Its own saved analysis and interpretation |
| Sensitivity | Changed thresholds, affected cases and conclusions |
Methods writing outline
We examined three collaboration conditions in 144 fictional businesses. Raw assessment scores were calibrated with [anchors and rationale]. The baseline used frequency [value], consistency [value] and PRI [value]. We inspected necessity separately and calculated outcome presence and absence as distinct questions. We compared [specified threshold alternatives].
Step 10. Write the result for this teaching file
We calibrated 144 synthetic cases using direct logistic calibration with anchors 2, 4 and 6 and inclusion membership 0.95. We used a frequency requirement of 2, row consistency of 0.80 and PRI of 0.50. We retained the conservative solution family.
Report the complete selected alternative and the changes shown in the sensitivity table. Explain case examples alongside aggregate coverage. These results describe the original teaching dataset, not the source paper’s observations. If several alternatives exist, explain the selection and preserve the others; do not combine favourite terms.
Explain the eight-pattern exercise without relying on jargon
- Read AND and OR correctly.
- Explain why omitted does not mean absent.
- Calculate the membership of one conjunction by hand.
- Identify a case that weakens sufficiency.
- Keep necessity separate from frequent pathway appearance.
- State that this exercise does not reproduce the source paper's ordinal structural estimator.