Spatial analysis facilitates theoretical construction. Photo:TUCHONG

The concept of “space” plays a vital role in the study of international relations. In recent years, the widespread use of geospatial data and geographic information systems has deepened scholars’ understanding of the dimension of space, giving rise to a steady stream of theoretical and empirical work grounded in spatial analysis. This has significantly contributed to both the development of international relations theory and the advancement of empirical research.

Reimagining theory through spatial lenses

Spatial analysis as a theoretical construction can be traced back to 1888, when British statistician Francis Galton famously commented on the work of British anthropologist Edward Burnett Tylor at the annual meeting of the Royal Anthropological Institute in the United Kingdom. This exchange gave rise to what is now known as “Galton’s Question.” Galton observed that tribes and ethnic groups around the world often share similar customs and practices. When studying these ethnic groups, it is necessary to further explore to what extent the formation of their customs and habits is the result of mutual dependence or independent development. He posed a crucial question: To what extent are such similarities the product of mutual influence versus independent development? Do these cultural traits originate from a shared source, or do they converge over time through imitation and interaction among groups?

“Galton’s Question” prompted two distinct lines of explanation. The first is grounded in the notion of “spatial aggregation.” This perspective holds that cultural similarities may arise because different groups are subject to similar external influences. In this view, even if the groups develop their customs independently and without direct interaction, similar environmental or contextual factors may lead to comparable social customs and habits.

The second explanation centers on “spatial interdependence”—the idea that groups exert mutual influence on one another, leading to convergence or divergence in customs and behavioral patterns. While spatial aggregation and spatial interdependence may appear similar in empirical observation, both being descriptive explanations of phenomenological similarities, the mechanisms behind them differ substantially. Not all instances of spatial aggregation result from spatial interdependence; various mechanisms can account for observed dependencies. “Galton’s question” remains a foundational point of departure for theory-building in the social sciences and continues to inspire insightful and thought-provoking research.

Mapping influence: How spatial analysis works

From a spatial analytical perspective, social science data inherently possess spatial attributes to some extent. Even when the research focus is not explicitly spatial—for instance, in studies centered on individuals—these individuals are situated within spatial units such as countries, provinces, counties, or even specific organizations. The units of analysis are embedded in distinct geographic contexts, and in this sense, spatial factors are always present, though often overlooked.

Therefore, a basic premise that researchers must acknowledge is that all social science data are spatial in nature. A fundamental principle of spatial analysis is “Tobler’s First Law of Geography,” formulated by Waldo R. Tobler in 1970: Everything is related to everything else, but near things are more related than distant things. This law underscores the importance of “geographic adjacency”—that is, phenomena or events in close spatial proximity tend to exhibit stronger correlations than those farther apart. Although distant phenomena may still display certain similarities, these are typically weaker. An essential step in spatial analysis is linking spatial data to analytical units (e.g., countries or provinces), typically through a process known as “spatial merging.” For example, researchers studying the effect of natural resource distribution—such as oil—on localized violent conflict must align the geolocations of conflict events with the locations of resource sites.

A core component of spatial analysis involves defining and constructing a spatial weight matrix (W), which serves as the foundation for various analytical techniques, including exploratory spatial data analysis, tests of spatial autocorrelation, and spatial econometric modeling. Understanding how units are spatially related is critical, and the spatial weight matrix—a square N × N matrix—captures the connections between all units in the dataset. Defining spatial relationships involves determining the “proximity” between units, which can be based on direct geographic adjacency, physical distance, or the number of nearest neighbors (as in k-nearest neighbor algorithms). The choice of proximity criterion directly affects both the structure of the W matrix and the outcomes of the spatial analysis.

Researchers often mainly consider the first-order proximity, which includes only directly adjacent units. However, higher-order proximities—such as second-order and Nth-order proximity—can also be further considered, incorporating neighbors of neighbors, and so forth.

One of the key steps in spatial analysis is identifying spatial autocorrelation, which helps reveal patterns in the geographic distribution of spatial phenomena. Tools such as mapping and the Moran’s I statistic allow researchers to detect whether spatial clustering is present in the data. In a 2008 study on the diffusion of armed conflict, Halvard Buhaug and Kristian Skrede Gleditsch demonstrated that armed conflict, particularly from 2001 to 2005, were geographically concentrated in specific regions. The fact that neighboring countries often experienced similar levels of conflict suggests that violence can spill across borders—highlighting the “contagious” nature of armed conflict in spatial terms.

When distance distorts: Why methods matter

Spatial analysis becomes an essential tool when the attributes of research subjects exhibit spatial dependence or heterogeneity, or when results may be affected by omitted variables. Traditional statistical analysis typically assumes that observations are independently and identically distributed. However, when the attributes of one unit may influence those of another, conventional methods may fail to fully capture such spatial interdependence. Spatial analysis, by contrast, is well-equipped to identify and account for such spatial dependencies.

Spatial analysis also plays a crucial role in addressing spatial heterogeneity—the idea that the strength and direction of a given treatment effect may vary by geographic location. Policies or interventions can produce markedly different outcomes across regions. Spatial analysis techniques allow researchers to detect and interpret these variations, thereby yielding more nuanced and accurate findings.

It is also a powerful tool for mitigating bias caused by omitted variables. In geographical or spatial units of analysis, there are often latent factors that cannot be directly observed but that may nonetheless generate spatial autocorrelation among variables. By modeling these hidden influences, spatial analysis helps control for omitted variable bias, leading to more robust and reliable model results.

Beyond empirical applications, spatial analysis plays a distinctive role in theoretical construction and validation. When a phenomenon has significant spatial characteristics that are integral to its theoretical framework, spatial analysis enables researchers to systematically incorporate geographic or spatial dimensions into theoretical construction. Deeper engagement with spatial dependence and spatial heterogeneity allows not only for the testing of existing theories but also for the development of new theoretical propositions—thus advancing theoretical innovation in the field.

In short, when research questions involve spatial dependence, spatial heterogeneity, omitted variable bias, and the significance of spatial dimensions in theoretical construction, spatial analysis offers a powerful means of capturing and interpreting complex dynamics. In international relations research, spatial proximity and its mutual influence should be treated as a fundamental analytical point of departure. That said, not every theory or model warrants the use of spatial analysis. Although most social science data carry spatial attributes and proximity often implies stronger relationships, this does not mean that all international relations analyses must adopt spatial analysis.

Chen Chong is an associate professor from the School of Social Sciences at Tsinghua University.