QuickPLS What the method does
Calibration specifies what it means for a case to be fully in, fully out or at the crossover of a set. The chosen transformation should follow the concept and measurement scale. Different supported calibration methods encode different assumptions; neither a convenient distribution nor a favourable solution is sufficient justification for the anchors.
Fuzzy membership m(x) ∈ [0,1]. Where a fuzzy crossover is defined, m(crossover) = 0.5.
The exact mapping depends on the calibration method. A fuzzy crossover is maximum ambiguity about membership, not a missing value. A crisp threshold instead assigns 0 or 1. Inspect the mapping and cases near each boundary before relying on the calibrated set.
Data and analysis in QuickPLS
Provide raw condition and outcome measurements, meaningful anchor values and case identifiers. Existing memberships should not be recalibrated as though they were raw scores.
QuickPLS provides the calibration choices and case-level membership outputs. Review the selected curve and compare defensible alternatives as separate specifications.
Follow a worked example
The following example shows the data, settings and decisions for one analysis. Use the linked practice files to follow it. For your own study, keep the procedure and choose the variables, model and settings that fit your research question.
Download calibration.csv to begin. It contains 6 rows and 3 columns. The example below identifies the variables to use, their roles and any rows to exclude; not every column is an analysis variable.
Decide what belonging to the set means
Calibration translates a measurement into membership of a set, such as organisations with adequate resources. Start by explaining what counts as belonging, not belonging and being at the crossover between them. The procedure and its reference values, called anchors, should follow that meaning. Rescaling a column into a convenient numerical range does not provide the explanation.
Inclusive crisp calibration places each case fully in or out and includes the threshold on the declared side. Piecewise linear calibration connects three anchors with straight segments. Bell/plateau calibration gives strongest membership to a middle range, while Valley uses the opposite shape. Choose the shape that represents the concept before examining which solution it produces.
Prepare the original values and the reasons for the boundaries
Keep the raw values, ordered anchors and intended direction ready. For indirect calibration, supply assigned memberships for every nonmissing original input row. Explain how those assignments or anchors represent the set, rather than choosing them to improve the later fsQCA fit.
Inspect the memberships before calculating the solution
Load the saved study
Open Advanced calibration from a completed result. Select Owning study and Saved specification revision, then Load selected setup. Confirm the source columns and their roles.
Choose the calibration
Select Inclusive crisp, Piecewise linear, Bell/plateau, Valley or the named indirect binomial-logit procedure. Fill in its required choices and their meaning; the app does not infer the missing anchors for you.
Check original values against memberships
Choose Preview calibrated cases. Inspect the boundary cases and each set's membership values. For an indirect fit, also read its fitting information and diagnostics.
Check the analysis cases and truth table
Record the missing-value and exact-crossover decisions, then choose Preview calibrated truth table. Check which cases and configurations the analysis will use.
Save the named calibration and calculate
Choose Save calibration revision. Continue in the returned protected copy if one is created, then Calculate calibrated fsQCA from the saved revision.
Distinguish fitting the calibration from selecting analysis cases
The indirect binomial-logit procedure fits a relationship between raw measurements and explicitly assigned memberships. Inspect its fitted coefficients, predicted memberships, fitting rows, iterations and diagnostics. Iterations are the repeated fitting steps used to reach a stable answer. Constant inputs, separation or failure to converge require investigation. Separation is a pattern that prevents finite best-fitting coefficients. This fit uses all nonmissing input rows before later fsQCA exclusions.
Inspect exact .5 memberships and nearby cases in the preview. A crossover is a meaningful boundary, not a rounding error to move out of the way. Keep values unchanged unless you deliberately change the substantive calibration, or record an eligible exclusion with its reason. Save a defensible alternative as a new revision. The teaching anchors below illustrate behaviour; they do not justify boundaries in your own study.
Read the memberships and excluded cases before interpreting truth-table classifications or solutions. For an indirect calibration, also check the fitted coefficients and iteration information. A case may contribute to fitting the calibration but be excluded from the later set analysis; report those populations separately.
Preview calibrated cases should show k01 to k06 with original x and the memberships for the selected shape. Compare them with the hand table below, then inspect the saved crossover decisions before Preview calibrated truth table. A crisp-only image cannot show the other shapes or establish their case policies.
On a small screen, swipe the table sideways to see every column.
| Output | How to read it | What to check |
|---|---|---|
| Calibration procedure and anchors | Match crisp, piecewise, bell/valley or indirect settings to the set you intend to measure. | The teaching anchors are examples, not recommended cutoffs for your own data. |
| Preview calibrated cases | Check boundary values and identify the original case behind each membership. | A plausible-looking histogram does not replace checking individual membership values. |
| Indirect fit rows and diagnostics | Inspect assignments, coefficients, iterations and fit status for all nonmissing rows used in calibration. | If separation occurs or the fit does not converge, investigate the error before using fitted memberships. |
| Saved calibration revision | Keep the fsQCA result with the dataset, calibration and case decisions that produced it. | Calibration fitting occurs before later analysis exclusions. Changing those exclusions does not change the rows used for fitting. |
Compare the same raw values under different definitions
Use the synthetic raw-score and calibration CSVs, or a copy of Research choices and calibration. Compare the saved calibration examples with the original values. Keep each alternative under a separate name.
Try five definitions on six easy-to-check values
Open calibration.csv. Cases k01 to k06 have x values 0, 1, 2, 3, 4 and 5. Y already supplies outcome memberships 0.1, 0.2, 0.3, 0.7, 0.8 and 0.9. Imagine x measures resource adequacy for this exercise. That meaning is invented, and the alternative calibrations express different ideas about what adequacy means.
An increasing calibration treats more x as stronger membership. A bell or plateau treats a middle range as strongest. A valley gives greater membership to the extremes. Those are different conceptual claims. Decide which one fits the research meaning before comparing the resulting tables and solutions.
Select the matching saved calibration example
The project includes Inclusive crisp threshold 2; Piecewise anchors 0, 2, 5; Bell plateau anchors 0 through 5; Valley anchors 0 through 5; and Indirect binomial-logit assigned memberships. Choose the calibration study rather than the necessity or counterfactual dataset in the same project. Leave Y as its supplied outcome membership.
These anchors make the arithmetic easy to see. They are not established resource-adequacy cutoffs. For real data, explain full exclusion, the crossover and full inclusion using the meaning of the set. An observed minimum or a percentile does not automatically tell you where a substantive membership boundary should be.
Preview, explain the case decisions and save the revision
Load the intended calibration setup
Open the saved calibration result in fsqca_research_choices.qpls and choose Advanced calibration. Select the calibration.csv study and the named revision for the procedure you want to inspect, then Load selected setup. Confirm x as the condition input and Y as existing outcome membership.
What you should see: The selected setup identifies the raw variables and calibration method.
How to read it: Do not treat existing memberships as raw measurements.
Enter the chosen procedure's settings
Check the loaded procedure against its stated teaching choices: increasing Inclusive crisp uses threshold 2; Piecewise linear uses exclusion 0, crossover 2 and inclusion 5; Bell/plateau and Valley use the six anchors 0, 1, 2, 3, 4 and 5. The indirect binomial-logit example assigns 0.05, 0.20, 0.40, 0.60, 0.80 and 0.95 to k01 through k06. Keep Y as supplied membership and explain the chosen definition. These are separate revisions, not settings to combine.
What you should see: The anchors and method-specific settings match the substantive set definition.
How to read it: Check their order and units.
Read each original value and membership
Choose Preview calibrated cases. Compare the original x with its membership, especially at the boundaries. Identify exact 0.5 values rather than assuming every case is clearly above or below the crossover.
What you should see: Original values are paired with calibrated memberships.
How to read it: Inspect cases near the crossover and anchors.
Check the exclusions for this calibration
Keep Missing values set to Reject missing input. Inclusive crisp and indirect binomial-logit have no crossover exclusions. Piecewise excludes original source row 3 (k03). Bell/plateau and Valley each exclude rows 2 and 5 (k02 and k05). These cases have membership exactly 0.5 under the respective calibration.
What you should see: The inclusion decisions match this calibration.
How to read it: A case can require a new decision when its membership changes.
Record a missing case decision
Under Explicit exact-crossover case decisions, inspect each Original source row and Reason. The saved reason is: Teaching choice: exclude this exact crossover for the stated analysis; original data remain retained. If an entry is missing, enter its row and reason, then choose Add explicit case decision. Keep existing entries and do not move a membership away from 0.5.
What you should see: The missing-case decision is recorded with its reason.
How to read it: It is separate from a deliberate crossover exclusion.
Preview the calibrated truth table
Keep Y as existing outcome membership and analyse its presence, with case_id as the case label. Each saved calibration uses frequency 1, consistency 0.80 and PRI 0.50, with no optional contradiction band or directional expectations. Choose Preview calibrated truth table and check the included cases against the recorded exclusions. The crisp and indirect revisions include all six cases; piecewise includes five; bell and valley each include four. Refresh both previews if you edit the settings.
What you should see: The preview uses the prepared memberships and intended cases.
How to read it: Verify the condition order before calculating.
Save and calculate that calibration
Choose Save calibration revision, continue in the returned protected copy when applicable, then Calculate calibrated fsQCA. Keep each calibration under its own name so the saved result remains connected to its choices.
What you should see: The saved result retains this calibration.
How to read it: Compare alternatives as separate results rather than overwriting the baseline interpretation.
Check the crisp threshold and the straight-line segments
For increasing inclusive crisp calibration at threshold 2, x = 1 is outside and x = 2 is inside. The six memberships are 0, 0, 1, 1, 1, 1. Inclusive means the value exactly at the threshold belongs on the selected side. Thus k03 is in the set; the rule is not strictly greater than the threshold.
With piecewise anchors 0, 2 and 5, membership rises from 0 at x = 0 to 0.5 at x = 2, then to 1 at x = 5. The six memberships are 0, 0.25, 0.5, 2/3, 5/6 and 1. Values beyond the outer anchors stay at the corresponding extreme. Case k03 is exactly at the crossover, so apply the explicitly chosen case policy. These values are hand calculations from the stated anchors.
On a small screen, swipe the table sideways to see every column.
| x | Inclusive crisp at 2 | Piecewise 0, 2, 5 | Bell/plateau | Valley |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0.25 | 0.5 | 0.5 |
| 2 | 1 | 0.5 | 1 | 0 |
| 3 | 1 | 2/3 | 1 | 0 |
| 4 | 1 | 5/6 | 0.5 | 0.5 |
| 5 | 1 | 1 | 0 | 1 |
Explain why a middle range would belong most strongly
For bell/plateau anchors 0, 1, 2, 3, 4 and 5, the memberships are 0, 0.5, 1, 1, 0.5 and 0. The middle values fully belong. The valley is the complement: 1, 0.5, 0, 0, 0.5 and 1. Cases k02 and k05 are crossover cases in both shapes.
A bell-shaped resource concept needs a reason why too little and too much both imply weak membership. A valley needs a reason why the extremes belong and the middle does not. The CSV cannot supply either reason. Changing the shape after seeing which produces a tidier solution changes the hypothesis, so explain that change if it is part of exploratory work.
Read assigned targets separately from fitted memberships
The indirect example assigns 0.05, 0.20, 0.40, 0.60, 0.80 and 0.95 to the six original observations. The binomial-logit procedure fits the relationship between x and those assignments. They guide the fitted curve; the resulting predicted memberships need not equal each assignment exactly.
The supplied saved fit has intercept -2.5833092849663952 and slope 1.033323713986558, with seven iterations and six fitting observations. These coefficients describe the relationship on a logit scale, a transformed scale used to fit memberships. They are not membership values themselves: a negative intercept does not mean negative membership. Read the predicted memberships to see how the fitted curve translates each raw value. These are existing saved values, not a fresh fit for this tutorial. Fitting uses the nonmissing original observations before later analysis exclusions, so an excluded fsQCA case may still have helped fit the calibration. Investigate constant x, separation or nonconvergence before using a failed fit.
Check the concept first, then the solution
When comparing revisions, keep the outcome definition and case rules clear. First decide whether the memberships represent the intended set. Then inspect their truth table and solution. If different crossover values change the included cases, report that alongside the difference in fit.
The indirect option is the specifically named binomial-logit procedure. A different fitting family in another package is a different method, even if both are called indirect calibration. If this fit is unsuitable, revisit its assumptions and membership assignments. Name the procedure actually used in the report.
Start with the original case and its calibrated value
When the analysis looks unexpected, inspect the raw value, selected procedure and membership before changing a threshold. The checks below help separate a boundary-rule misunderstanding from an unsupported conceptual choice or a fitting error.
On a small screen, swipe the table sideways to see every column.
| Symptom | Check | Action |
|---|---|---|
| x = 2 differs from expectation | Whether crisp calibration is inclusive | Apply the stated inclusive threshold and explain the boundary. |
| Some cases sit exactly at 0.5 | The piecewise or bell/valley anchors | Record an explicit crossover policy before calculating. |
| A bell result reverses the increasing result | The concept represented by the set | Choose the shape from the meaning of the concept and the reasons for its boundaries, rather than the fit you prefer. |
| Indirect predictions differ from assignments | Whether the display shows targets or fitted memberships | Report both roles and the actual saved fit. |
| Indirect fitting fails | Variation in x, separation and convergence information | Investigate the fit and assignments; do not treat failure as zero membership. |
Describe the membership rule precisely enough to repeat it
State the procedure, direction, anchors or assignments, and reasons for the boundaries. Report how exact crossovers and missing values were handled. For the indirect procedure, distinguish the fitting rows and diagnostics from the cases included in the final fsQCA analysis.
On a small screen, swipe the table sideways to see every column.
| Procedure | Setting to report | Numerical origin |
|---|---|---|
| Inclusive crisp | Increasing; threshold 2; inclusive | Hand membership calculation |
| Piecewise | Anchors 0, 2, 5 | Hand interpolation |
| Bell and valley | Six anchors 0 through 5 | Hand membership calculation |
| Indirect binomial-logit | Six assigned memberships; fitted coefficients | Existing saved calibration fit |
Example Methods paragraph
For the synthetic calibration exercise, we compared named procedures with explicitly stated anchors. The piecewise specification used exclusion 0, crossover 2 and inclusion 5; the inclusive crisp specification used threshold 2. We inspected resulting case memberships and recorded crossover decisions before interpreting the set analysis.
Describe how the set changed
You could report: Crisp calibration placed k03 fully inside the set, while piecewise calibration placed it at the crossover. Bell and valley calibrations placed k02 and k05 at the crossover and expressed opposite middle-range hypotheses. The supplied indirect fit used six observations and converged in seven iterations. These differences concern how the set was defined; they do not establish that one procedure is always preferable.
- Calculate a membership between two anchors by hand.
- Locate every exact crossover for the chosen shape.
- Explain the anchors using the meaning of the research concept.
- Distinguish indirect assignment targets from fitted memberships.
- Name the saved calibration revision used for the reported analysis.
Keep exact crossover values and investigate fitting errors
The indirect procedure fits every nonmissing assigned input row before applying later analysis exclusions. Investigate separation or nonconvergence before using predicted memberships. Do not nudge an exact .5 value just to place it on one side of the crossover.