Queen ContiguityEdit
Queen contiguity is a practical rule used in the analysis of areal data to define which regions are considered neighbors. Under this scheme, two areas are neighbors if they touch each other at any point along an edge or at a corner. The neighbors are encoded in a spatial weights matrix W, where w_ij = 1 if areas i and j share a boundary or a vertex, and w_ii = 0 to avoid self-neighborhood. In many applications, the rows of W are row-standardized so that the weights sum to one, making the spatial lag a weighted average of neighboring values. This straightforward idea sits at the core of modern spatial statistics and geography, and it is a staple in fields such as spatial econometrics and geographic information system.
Overview
Queen contiguity is one of several contiguity schemes used to model how nearby regions influence each other. It extends the simpler rook contiguity, which only considers shared edges, by also including shared vertices. This broader sense of adjacency can be especially important in densely packed regions where share points matter for diffusion processes or localized spillovers.
In practice, researchers use queen contiguity to construct spatial lag models and spatial error models. In a spatial autoregressive framework, for example, the predicted value in one area incorporates a weighted average of neighboring values, as determined by W. This makes queen contiguity a natural fit for analyzing diffusion-like phenomena, where effects propagate not just along clear borders but also through close contact at corners or intersections.
Key technical terms connected to queen contiguity include spatial weights matrix, areal data, and spatial autoregressive model. For map-based analyses, practitioners often consult geographic information system tools and libraries that implement these weights schemes, allowing them to experiment with alternative definitions such as rook contiguity or distance-based weights.
Construction and interpretation
Definition: A queen contiguity matrix W marks w_ij = 1 if areas i and j share any boundary point (edge or vertex); w_ii = 0. This captures a broad neighborhood concept, suitable for problems where contact could occur through corners or at shared nodes in a tessellated map.
Variants: Analysts may row-standardize W so that each row sums to one, transforming the matrix into a form where the spatial lag is a weighted average of neighbors. Alternatives include keeping raw counts or applying distance-based decay factors in combination with contiguity rules. See also spatial weights matrix and row-standardization for deeper discussion.
Relation to other schemes: Queen contiguity sits alongside rook contiguity (which ignores vertex-only contacts) and various distance-based or k-nearest-neighbor frameworks. Each choice reflects assumptions about how strongly geography translates into interaction, and the selection should align with the substantive context of the study.
Interpretation cautions: The meaning of a “neighbor” in queen contiguity rests on administrative boundaries and geographic tessellations. It is a convenient, interpretable proxy for potential interaction, but it is not a direct measure of social ties, trade, or traffic unless supplemented by additional data.
Applications and case studies
Regional spillovers: Queen contiguity is frequently used to study how policy changes or economic shocks in one jurisdiction influence neighboring areas. By incorporating the spatial lag, researchers can quantify indirect effects that go beyond a region’s own characteristics. See spillover effects and diffusion in geography and economics literature.
Urban and regional economics: Analysts apply queen contiguity to questions about how urban amenities, housing prices, or employment shocks diffuse across nearby municipalities or counties. This is common in studies of economic geography and regional science.
Cross-border and intergovernmental analyses: In places where administrative boundaries are close or where functional interactions cross borders, queen contiguity helps capture potential diffusion across jurisdictions, without requiring detailed data on every contact or flow.
Policy evaluation: When evaluating the impact of local policies, researchers may use queen contiguity to account for neighboring-policy spillovers that could bias simple, unit-level estimates if ignored. This is particularly relevant for environmental regulation, infrastructure investments, or taxation regimes.
Strengths, limitations, and debates
Strengths: The queen contiguity approach is simple, transparent, and easy to implement in standard econometric frameworks. It provides a defensible, localized notion of interaction that aligns with intuitive geographic proximity in many map-based analyses. The method is robust to small changes in data structure and is easy to communicate to policymakers and stakeholders.
Limitations: The choice of contiguity (queen vs. rook vs. distance-based schemes) can materially affect results. The approach assumes that all touching regions exert equal influence, once standardized, which may not reflect real-world interaction patterns such as varied population, trade intensity, or transportation links. This sensitivity is a central concern in discussions about the method.
MAUP and scale: As with many areal-data techniques, queen contiguity is subject to the modifiable areal unit problem (MAUP). Different zoning or aggregation schemes can lead to different inferences about diffusion and spillovers. Sensitivity analyses with alternative weight structures are recommended to check robustness.
Controversies and debates: Critics sometimes argue that adjacency-based models embed arbitrary political boundaries into analyses of social and economic processes, potentially masking more meaningful interaction networks like trade routes or commuting patterns. Proponents respond that, in the absence of perfect data on flows, a clear and interpretable proximity rule provides a stable baseline for inference and policy discussion. When results hinge on the exact neighbor definition, researchers should test multiple specifications (e.g., queen contiguity, rook contiguity, and distance-based weights) and report how conclusions change.
Political and methodological critiques: Some critics emphasize that spatial models can be used to justify interventions or to attribute effects to places in ways that ignore local context or governance differences. From a pragmatic standpoint, the refutation is that a transparent, well-documented weighting scheme—like queen contiguity—helps policymakers separate localized effects from broader regional trends. If a study is sensitive to the chosen weights, the responsible move is to disclose this sensitivity and test alternatives, not to abandon the method.