Data, Spatial

Spatial Relations

One way to appreciate the importance of spatial patterns in data is to consider the analogy to time-series data. Researchers are increasingly sensitive to how individual data points collected over time often will not be independent of one another, as many social and political processes display clear [Page 521]trends and persistence over time. To use a concrete example, consider how people's evaluations of an incumbent government typically change slowly over time. Data on approval taken at two points that are close in time are thus likely to display similar values or serial correlation. It would be misleading to consider the individual observations a random sample, and analysts will need to take into account their temporal ordering if they want to examine how other features such as economic performance may influence changes in approval. If economic performance is believed to influence approval and such data also display a trend over time, then analysts risk making spurious inferences if they do not take into account the possibility of serial correlation.

Social science researchers have been much less attuned to the possibility that data collected for units at the same point in time may not be independent of one another across space. Francis Galton pointed out in an early influential comment on an article comparing marital institutions across societies that the observed outcomes could result from diffusion between societies rather than independent processes operating in isolation in each unit. Stated differently, common marital institutions may not reflect a functional relationship to certain shared social characteristics, as implied by the author of the article Galton commented on, but could stem from a diffusion process in which societies may be likely to adopt the institutions found in other societies that they interact with. Distinguishing between the results of independent outcomes within each unit and diffusion may be difficult, hence the term Galton's problem. For example, societies that interact more with one another may be similar in other respects, such as in economic or other social structures. Analyzing the observations as independent units and looking for functional relationships between social characteristics and marital institutions would run the risk of making unwarranted inferences about causal relationships from social characteristics to marital institutions, unless the possibility of diffusion or spatial dependence among units is taken into account.

There are many reasons to suspect that political and social phenomena often reflect diffusion or spatial dependence, in the sense that observations that are “near” or “connected” in some manner tend to have similar values. For example, individual attitudes may not just reflect an individual's own characteristics but could also be influenced by the people that this person interacts with. As such, two individuals who are connected by common ties may have similar attitudes, even if they at a first glance would seem very different on other social characteristics. Likewise, policies and institutions may be influenced by the policies and institutions adopted by other states. For example, the prospects for democratic reform in autocracies may be influenced not just by domestic events and characteristics but also by international ties and events in other states. Likewise, certain policies such as smoking bans have evolved from being perceived as an extreme form of legislation to become a mainstream policy adopted by many states with very different characteristics. Beth Simmons, Frank Dobbin, and Geoffrey Garrett provide a typology of different diffusion mechanisms for policies and institutions, distinguishing between coercion, competition, learning, and emulation. Attention to spatial dependence can be very helpful in learning new insights or developing new hypotheses about the phenomenon of interest. However, it is unlikely that a single theory of diffusion or spatial dependence will be generally applicable, and such theorizing is probably best done on a case-specific basis.

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