Selection–Transmission Sensitivity Analysis¶
Robustness analysis — instantiates Selection–Transmission Change Attribution
Re-runs the selection–transmission split under alternative windows, unit definitions, and weighting schemes to report how stable the verdict is before it drives a decision.
A single decomposition gives one split; whether that split is real or an accident of arbitrary choices is a different question. Selection–Transmission Sensitivity Analysis answers it by re-running the split under alternative windows, unit definitions, and weighting schemes and recording how much the verdict moves across them. Its defining product is not a point estimate but a register of the range — the distribution of selection and transmission terms across defensible specifications, and a statement of how stable "selection dominates" (or "transmission dominates") actually is. It computes no single authoritative split and routes no action; it stress-tests a split someone else computed, so that a conclusion is stated as robust or fragile rather than as settled fact.
Example¶
An analyst finds that a basketball league's average three-point attempt rate rose sharply across two seasons, and the base decomposition attributes most of it to selection — high-volume shooting teams gained games and weight. Before publishing "the league's mix changed, not its teams," they run the sensitivity analysis. They shift the comparison window by half a season; they treat relocated and expansion franchises alternately as new units and as continuing ones; they weight by games played, then by minutes, then by possessions. Across these specifications the selection share ranges from 45% to 80%. The "selection dominates" verdict holds under most choices but flips to transmission-dominant under possession-weighting. The register records that fragility, and the published claim becomes conditional — "selection-led under most reasonable specifications, but sensitive to how team activity is weighted" — rather than a single confident number.
How it works¶
Enumerate the analytic choices that are defensible but arbitrary: window placement and width, the unit and correspondence rule, the weighting scheme, and how entrants are handled. Re-run the decomposition under each combination and record the resulting selection and transmission terms as a distribution — the variance-and-response-capacity register. Report the modal verdict, the share of specifications that agree with it, and which single choice the split is most sensitive to. The method is a specification-curve or multiverse sweep applied to the selection–transmission split: rather than defend one pipeline, it shows the conclusion across many and lets the spread speak.[n1]
Tuning parameters¶
- Specification breadth — how many analytic choices are varied and how many levels each. Wider sweeps are more honest about fragility but cost more and can overwhelm a decision that a stable core already settles.
- Flip criterion — how large a change in the dominant term counts as the verdict "flipping." A strict criterion reports more stability; a loose one flags fragility sooner.
- Reporting statistic — whether robustness is summarized as a full range, an interquartile band, or the share of specifications agreeing. Each trades completeness against a single communicable headline.
- Pre-registration — whether the specification set is fixed before results are seen. Pre-declaring it guards against cherry-picking; deciding it afterward invites the garden of forking paths.
When it helps, and when it misleads¶
Its strength is converting a fragile single split into an honesty statement: it catches conclusions that live only in one arbitrary slicing and gives a decision-maker the range, not a falsely precise point.
Its failure mode is that a large specification space can be cherry-picked to support any verdict — the garden of forking paths, where the flattering corner is reported as if it were the whole sweep — or, at the other extreme, an exhausting all-specifications sweep can paralyze a decision that a stable core would have settled cleanly. The classic misuse is running the analysis, finding the split holds under most choices, and still highlighting the one specification that flips it to fit a prior. The guarding discipline is to pre-declare the specification set, report the full distribution rather than a chosen slice, and let the modal verdict and its agreement share — not the most convenient corner — carry the conclusion.
How it implements the components¶
variance_and_response_capacity_register— the recorded distribution of selection and transmission terms across specifications, quantifying how much the verdict can move.state_pair_or_transition_window— it varies the window and state-pair placement as one of the swept analytic choices.counterfactual_weight_or_value_baseline— it varies the weighting and baseline conventions as another swept choice, mapping how the split responds to each.
It routes no action from the result (intervention_attribution_rule — that is the Composition-vs-Transformation Dashboard) and it produces no base recomposition (decomposition_identity_and_residual_check — that is the Price Equation Decomposition Table). Its nearest twin is the dashboard: this analysis stress-tests whether the split survives alternative choices, while the dashboard communicates a single split and routes it to a lever — the separating component is the robustness register it owns versus intervention_attribution_rule.
Related¶
- Instantiates: Selection–Transmission Change Attribution — it supplies the robustness check the archetype demands before high-stakes claims.
- Consumes: Price Equation Decomposition Table supplies the base split this analysis re-runs under alternative specifications.
- Sibling mechanisms: Price Equation Decomposition Table · Covariance Selection-Term Calculation · Within-Unit Change Assay · Lineage or Panel Correspondence Matrix · Composition-vs-Transformation Dashboard · Entry/Exit Normalization Protocol · Decomposition Residual Reconciliation Workflow
Editorial Notes¶
Form Classification¶
Form family: Analysis, Modeling & Optimization
Rationale: Selection–Transmission Sensitivity Analysis operates as an analytical, modeling, inference, comparison, or optimization procedure that derives insight or a solution because it re-runs the selection–transmission split under alternative windows, unit definitions, and weighting schemes to report how stable the verdict is before it drives a decision.
Independent corroboration: The frozen evidence defines Selection–Transmission Sensitivity Analysis as 'Re-runs the selection–transmission split under alternative windows, unit definitions, and weighting schemes to report how stable the verdict is before it drives a decision', so its operative form is Analysis, Modeling & Optimization.
Review outcome: Independent reviewer agreement; high confidence.
Origin Attribution¶
Primary origin: Statistics & Experimental Design
Origin pattern: Cross-disciplinary synthesis
Present-day reach: Multi-domain
Rationale: Re-estimating a decomposition under alternative windows, units, and weights is statistical robustness and sensitivity analysis.
Related originating lineages:
- Biology & Ecology — Separating selective survival from transmission is rooted in evolutionary population accounting.
- Data Science & Analytics — Pipeline robustness checks routinely vary feature windows, aggregation units, and weighting conventions.
- Mathematics — Mathematical modeling, proof, and abstract-structure practice supplies a parallel or contributing lineage for the mechanism's defining operation: re-runs the selection–transmission split under alternative windows, unit definitions, and weighting schemes to report how stable the verdict is before it drives a decision.
Review resolution: The blind reviewers agree that statistics_experimental_design is the primary origin and differ only on reported ambiguity, alternate origin disagreement. I preserve every independently explained alternate from both records rather than imposing a numeric cap. I retain cross_disciplinary_synthesis because the combined record shows material contributions from several lineages. The broader reach of multi_domain records portability separately from historical provenance, and encyclopedia_synthesis=true preserves the affirmative synthesis judgment where either reviewer identified one.
Attribution caveat: The selection-transmission decomposition is domain-specific, but the stability protocol is statistical.
Encyclopedia synthesis: The exact catalogued form synthesizes established practice rather than reproducing a single standard historical label.
Review outcome: Reconciled after independent review; medium confidence.
Notes¶
[n1] Specification-curve (or multiverse) analysis runs an estimate across the full set of defensible analytic choices and reports the distribution of results rather than a single pipeline's number. Applied here, it turns "selection dominates" from a claim about one decomposition into a claim about how that decomposition behaves across every reasonable way of drawing it. ↩