Selection Transmission Change Attribution

When an aggregate mean changes, split the change into how much came from units gaining or losing weight and how much came from units changing internally.

Working definition

Selection–Transmission Change Attribution explains a change in a weighted population mean by separating two channels that are easy to confuse. The selection channel changes the aggregate because units gain, lose, enter, exit, survive, expand, shrink, or otherwise change weight. The transmission channel changes the aggregate because continuing or linked units change their own values.

This matters because the same aggregate movement can demand different interventions. If the selection term dominates, the system changed because the mix of units changed. If the transmission term dominates, the units themselves changed. If the terms have opposite signs, the aggregate may be masking one channel with the other.

When to use it

Use this archetype when an average, rate, trait, score, or capability changes over time and the units behind the aggregate have both weights and values. The pattern is especially useful when response choices differ across levels: change admission, retention, portfolio mix, survival pressure, or exposure if selection dominates; change training, repair, learning, adaptation, process design, or transmission pathways if within-unit change dominates.

Do not use it as a generic synonym for decomposition. It requires a weighted mean, a comparison across states, and a meaningful distinction between unit weights and unit values.

Core components

Component	Description
Population Unit and Scope Definition ↗	The population must be bounded and the units must be named. In evolutionary settings, the units may be lineages or variants. In organizations, they may be teams, products, clients, cohorts, or assets. In policy analytics, they may be regions, households, institutions, or cases. The unit rule determines what can count as selection and what can count as transmission.
Unit Value Measure ↗	The value measure is the trait, score, payoff, performance level, risk, or state being averaged. It must be comparable across the two states. If the measure changes definition halfway through, the transmission term may become a measurement artifact.
Unit Weight Measure ↗	The weight measure tells how much each unit contributes to the aggregate. Weights may represent frequency, survival, population share, revenue share, exposure, market share, case load, representation, or influence. The selection term is about changes in these weights.
Unit Correspondence Map ↗	The correspondence map links units across states. It records continuing units, new units, exited units, split units, merged units, and descendant units. Without this map, the analysis cannot reliably distinguish a unit changing internally from one unit being replaced by another.
Selection and Transmission Term Definitions ↗	The selection term accounts for aggregate change due to differential weighting. The transmission term accounts for aggregate change due to within-unit value change. Both terms must be defined in a way that recomposes to the observed aggregate change, with residuals explicitly investigated.

Common mechanisms

A Price Equation Decomposition Table is the canonical mechanism when the data support exact unit-level accounting. A Covariance Selection-Term Calculation is useful when the selection term can be expressed as covariance between unit value and relative weight change. A Lineage or Panel Correspondence Matrix helps operationalize unit continuity across states. A Composition-vs-Transformation Dashboard makes the split legible to decision-makers. A Residual Reconciliation Workflow keeps unmatched units, measurement drift, and normalization errors from being interpreted as substantive change.

Invariants to preserve

The most important invariant is recomposition: the reported terms plus declared residuals must recover the observed weighted-mean change. The second invariant is separation: unit values and unit weights must not collapse into one informal story. The third invariant is reviewability: another analyst should be able to see how units were matched, how weights were normalized, and how entry or exit was handled.

Boundary distinctions

This archetype is adjacent to aggregation-bias correction, but it is not the same thing. Aggregation-bias work asks whether an aggregate summary misleads relative to subgroup or partition structure. Selection–Transmission Change Attribution asks why an aggregate changed across states.

It is also adjacent to generic decomposition, but it is narrower and more exact. The decomposition is not arbitrary; it is organized around weighted population means, differential unit weights, and within-unit value change.

It can use panel or time-series data, but it is not equivalent to time-series cross-section analysis. Panel analysis supports many statistical questions; this archetype is specifically about attributing weighted-mean change between selection and transmission channels.

Examples

In evolutionary dynamics, a trait mean can rise because high-trait lineages leave more descendants and because descendants shift trait values relative to parents. In a company, average productivity can rise because high-performing units grow headcount, because each unit improves, or both. In education, a school’s average test score can rise because the cohort changed or because continuing students learned more. In product analytics, average engagement can rise because heavy users become a larger share, not because each segment became more engaged.

Failure modes

The most common failure is treating aggregate improvement as within-unit improvement when it is really composition change. The second is treating a mathematical split as causal proof. The third is hiding attrition or exclusion inside a favorable aggregate. The fourth is using the decomposition despite weak unit correspondence or drifting measurement scales.

Review note

The draft should be reviewed against aggregation_bias_detection_and_correction, aggregation_function_design_and_weighting, solvable_baseline_decomposition, and future coverage of variance_bounds_selection_response. The current disposition check supports a full draft because no accepted archetype or prior queue output directly covers the exact selection/transmission split.

Common Mechanisms

• Composition-vs-Transformation Dashboard
• Covariance Selection-Term Calculation
• Decomposition Residual Reconciliation Workflow
• Entry/Exit Normalization Protocol
• Lineage or Panel Correspondence Matrix
• Price Equation Decomposition Table
• Selection–Transmission Sensitivity Analysis
• Within-Unit Change Assay

Compression statement

Selection–Transmission Change Attribution is the intervention pattern for explaining a weighted-mean shift by explicitly separating differential representation of units from within-unit transformation, then routing action to composition, selection pressure, retention, learning, repair, or measurement according to the dominant term.

Canonical formula: Δ mean ≈ selection_term + transmission_term; selection_term tracks differential unit weights, transmission_term tracks within-unit value change, with residuals audited for unmatched units and measurement drift.

Related Abstractions

Abstractions this archetype builds on — directly (a source ingredient) or as a related pattern. Links follow the typed catalog namespace.

Built directly on (4)

• Aggregation: Deliberately collapsing many items into a single summary, choosing which information to discard to gain tractability.
• Decomposition: Breaking a whole into parts that can be analyzed independently and recombined to reconstitute the whole, making complexity tractable through divide-and-conquer.
• Natural Selection: A population of varying, heritable variants is filtered by a selection pressure so that the better-performing variants differentially reproduce or persist, shifting the population's composition over rounds — variation, selection, and retention as a substrate-neutral engine.
• Selection Vs Transmission Decomposition: A change in a population's weighted mean splits exactly into a selection term (differential weighting of units) and a transmission term (units changing within themselves).

Also references 16 related abstractions

• Causality: Cause-effect relationships.
• Comparison: Place items in a shared frame along chosen dimensions to read off a relation between them.
• Data Integrity: Accuracy and consistency preserved.
• Diversification: Spreading exposures across positions whose failure modes are uncorrelated reduces total-outcome variance; correlation, not count, drives the benefit.
• Effect Size: Magnitude of effect.
• Invariance: Properties unchanged under transformation.
• Modifiable Areal Unit Problem: Statistics computed on aggregated data change, sometimes reversing sign, when the boundaries used to aggregate are redrawn — the partition is a non-neutral analytical input.
• Partition Dependence of Aggregates: Any statistic computed on partition-aggregated data is a function of the partition itself, not solely of the underlying data.
• Proportionality: Match response to scale.
• Scale: Properties change with size.

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Variants

Narrower or domain-specific specializations that share this archetype's core structure. Recognized variants are established; candidate variants are provisional.

Price Equation Attribution · method family variant · recognized

A formal variant using the Price-equation style identity to split aggregate change into covariance/selection and expectation/transmission terms.

• Distinct from parent: The parent includes any practical selection/transmission attribution; this variant emphasizes the canonical Price-equation mathematical form.
• Use when: The population can be represented as units with weights and values across states; Differential persistence or representation and within-unit change are both plausible causes of aggregate change.
• Typical domains: evolutionary dynamics, organizational analytics, economics
• Common mechanisms: price equation decomposition table, covariance selection term calculation, selection transmission sensitivity analysis

Composition-vs-Capability Change Split · domain variant · recognized

A management and analytics variant that asks whether an aggregate metric changed because the mix of units changed or because each unit improved or degraded.

• Distinct from parent: The parent is cross-domain and includes evolutionary lineages, epidemiology, economics, and learning systems.
• Use when: A portfolio, team, customer base, fleet, or cohort changes average performance across periods; The decision response differs depending on whether the driver is mix shift or within-unit transformation.
• Typical domains: organizational management, product analytics, public policy
• Common mechanisms: composition vs transformation dashboard, entry exit normalization protocol, decomposition residual reconciliation workflow

Selection-Response Bounds Linkage · scale variant · candidate

A variant that connects the observed selection term to available variance and selection intensity so expected response bounds can be checked.

• Distinct from parent: The parent attributes current aggregate change; this variant adds response-bound interpretation over repeated selection rounds.
• Use when: The selection contribution is large enough that available variance may constrain future response; A system is being managed for adaptive response over repeated rounds rather than a single before/after attribution.
• Typical domains: breeding, algorithmic selection, portfolio management
• Common mechanisms: covariance selection term calculation, selection transmission sensitivity analysis

Near names: Selection Vs Transmission Decomposition, Price Equation Decomposition, Between–Within Change Decomposition, Composition–Transformation Split, Weighted Mean Change Decomposition.