aggregatability

Aggregatability is a property of a statistic or model describing whether information lost when data are aggregated can be recovered, or whether aggregate measures faithfully reflect the underlying micro-level structure. In practice, it concerns whether a macro-level summary—such as a mean, a probability, or a model parameter computed from pooled data—can be derived from, or is consistent with, the corresponding micro-level quantities.

Many systems are not aggregatable. Aggregation can obscure heterogeneity or interactions, so the aggregate may not reflect the behavior of its parts. For example, the overall average of outcomes is not necessarily equal to the average of group means if groups differ in size or composition. The Simpson’s paradox illustrates how a relationship can reverse or vanish after aggregation, highlighting potential non-aggregatability.

Conditions for aggregatability include linearity and homogeneity. If the statistic is linear (additive) and the micro-level units share a common structure with no interactions between units, aggregation can commute with the statistic. More generally, aggregatability holds when the aggregation mapping and the micro-level model are compatible, or when a multilevel framework properly accounts for heterogeneity across units.

Fields in which aggregatability matters include statistics, econometrics, epidemiology, sociology, and demography. It is a core consideration in ecological inference, where researchers attempt to infer individual behavior from aggregate data. Recognizing aggregatability helps prevent ecological fallacies and misinterpretation of policy effects. When aggregatability is in doubt, analysts may rely on microdata, stratified analysis, or multilevel models to preserve the fidelity between aggregated summaries and their constituent units.