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A consensus mechanism map can look stable because one influential protocol holds several uncertain observations together. Leave-one-out partition diagnostics remove each protocol in turn, refit the model and ask what changes: pairwise co-clustering, group count, boundary assignments and the scientific action based on the map.
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Chapter contents
Choose the route closest to the decision, or read from Chapter 1. The chapters remain open; these grouped routes are a navigable index.
Route 1 · Define the decision
Route 2 · Work the ledgers
Route 3 · Transfer the method
Route 4 · Check limits and evidence
Route 5 · Ask and continue
CHAPTER 1 OF 12 · DEFINE THE DECISION
1. Influence concerns the analysis, not personal blame
A protocol can be influential because it occupies a rare temperature, chemistry or loading condition. That does not make it wrong. Influence says the fitted partition or decision changes materially when its evidence is removed.
Separate leverage, measurement quality and scientific importance. A unique condition may be both highly influential and essential to the study’s scope.
CHAPTER 2 OF 12 · DEFINE THE DECISION
2. Leave one protocol out and repeat the full pipeline
For protocol i, remove all observations that belong to that protocol, refit the class-count and partition model, reconstruct the posterior similarity matrix and recompute the consensus partition under the same loss.
Do not merely delete one row from the final heat map. Priors, component parameters and uncertainty must be updated because the omitted protocol may have influenced every other assignment.
CHAPTER 3 OF 12 · WORK THE LEDGERS
3. A protocol-influence ledger
A polymer study contains five validation protocols. The diagnostic compares the full posterior similarity matrix with each leave-one-out matrix on the remaining protocols.
| Omitted protocol | Matrix change | Consensus change | Mechanism decision |
|---|---|---|---|
| A: ambient cycle | 0.04 | None | Unchanged |
| B: high humidity | 0.11 | One boundary moves | Unchanged |
| C: rapid shear | 0.29 | Three to two groups | Changes |
| D: thermal hold | 0.08 | None | Unchanged |
| E: recovery | 0.17 | Boundary widens | Review |
Protocol C requires investigation because its omission changes both the partition and the mechanism decision. Protocol E deserves review even though the selected group count survives.
CHAPTER 4 OF 12 · WORK THE LEDGERS
4. Worked fragility comparison
The full analysis reports groups AB, C and DE. After omitting C, the remaining protocols form AB and DE; after omitting E, D shifts between the two surviving groups.
| Summary | Full fit | Leave-C-out | Leave-E-out |
|---|---|---|---|
| Group count | 3 | 2 | 3 |
| AB co-clustering | 0.94 | 0.92 | 0.95 |
| D boundary probability | 0.36 | 0.18 | 0.51 |
| Release decision | Conditional | Release | Review |
Report the stable core and the fragile edge separately. Calling the whole map unstable would discard useful information; calling it stable would hide the decision reversal.
CHAPTER 5 OF 12 · WORK THE LEDGERS
5. Use more than one partition discrepancy
Compare posterior similarity matrices, expected partition loss, credible balls, group-count support and decision outputs. One scalar score cannot reveal whether instability is global, local or scientifically consequential.
Align comparisons on the retained protocols. When an omitted protocol defines an entire class, describe that loss explicitly instead of forcing a one-to-one group match.
CHAPTER 6 OF 12 · TRANSFER THE METHOD
6. Distinguish protocol influence from replicate influence
A protocol groups specimens under one acquisition or treatment rule. Removing one measurement estimates a different kind of sensitivity. Use grouped deletion when within-protocol observations share calibration, environment or operator effects.
If there are only a few protocols, leave-one-out estimates can be variable. Add parametric checks, alternative priors and targeted replication rather than treating deletion as a final causal verdict.
CHAPTER 7 OF 12 · TRANSFER THE METHOD
7. Changed-context transfer: humidity–temperature matrices
Transfer the method to a factorial ageing study. Removing one humidity–temperature cell can break interpolation support and shift the apparent degradation pathway.
The transfer check records whether the deleted cell is interior or at the edge of the design, whether missingness is structurally plausible and whether conclusions are intended only inside the tested region.
CHAPTER 8 OF 12 · TRANSFER THE METHOD
8. Connect the partition and hierarchy branches
The partition-stability guide defines posterior similarity matrices and consensus maps. The class-count guide covers split–merge uncertainty.
Use the mixture-hierarchy guide when one protocol changes how information is pooled across classes.
CHAPTER 9 OF 12 · CHECK LIMITS AND EVIDENCE
9. Limits and common misconceptions
Leave-one-out influence is not proof that a protocol is biased. It may expose a genuine but weakly replicated mechanism regime.
A consensus partition that stays identical can still be fragile if co-clustering probabilities or downstream decisions change substantially.
CHAPTER 10 OF 12 · CHECK LIMITS AND EVIDENCE
10. Practical evidence checklist
Archive the full and deleted datasets, random seeds, prior settings, posterior similarity matrices, group-count support, partition losses, decision maps and protocol metadata.
Predefine material-change criteria. Investigate influential protocols with raw measurements, calibration records and targeted replication before removing or down-weighting evidence.
CHAPTER 11 OF 12 · ASK AND CONTINUE
11. Frequently asked questions
Must the model be refitted for every omission?
Yes for a genuine deletion diagnostic. Reusing the full posterior can miss how the protocol changed global parameters and class support.
What if every protocol is influential?
The design may be too small for a stable mechanism map, or the system may be strongly heterogeneous. Report that dependence rather than manufacturing a robust partition.
Can influence guide new experiments?
Yes. Prioritise protocols whose replication is expected to resolve a decision-changing partition boundary.
CHAPTER 12 OF 12 · ASK AND CONTINUE
12. Sources and next reading
Fritsch and Ickstadt present posterior-similarity criteria for Bayesian clustering. Wade and Ghahramani develop partition point estimates and credible balls. Coleman and colleagues study consensus clustering for Bayesian mixture models. The polymer influence ledgers above are original teaching examples.
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