Spatial Heterogeneity

An Introduction to Spatial Heterogeneity

Spatial heterogeneity refers to the uneven distribution of a trait, event, or relationship across a region (Anselin, 2010). It is frequently introduced simultaneously with the term spatial dependence and, in practice, the two can be difficult to tease apart from each other. Whether we are dealing with spatial heterogeneity or spatial dependence can be influenced by the scale that we are considering and the research questions in which we are interested. Spatial heterogeneity is also sometimes referred to as sub-regional variation, parent contagion, first-order variation,” or first-order spatial effects. Conversely, spatial dependence is sometimes referred to as second-order spatial effects.

Spatial heterogeneity generally refers to the clumpy or patchy distribution of processes or events across a broad landscape, whereas spatial dependence refers to processes that create clusters of events, etc.  That is, spatial heterogeneity describes a patchy landscape and spatial dependence refers to the local non-independence of occurrences that are near each other. One way to think about these two concepts is to ask yourself: (a) Is the intensity of occurrence of an event equally distributed across the landscape? and (b) Does the intensity at one location influence the intensity at neighboring locations? If you answered yes to the first question you are dealing with spatial heterogeneity and if you answered yes to the second question you are dealing with spatial dependency. Furthermore, if a landscape has spatial heterogeneity it may be the result of spatial dependency. When considering demographic processes, spatial heterogeneity, rather than spatial homogeneity, is generally the norm. Even homogeneous environments are likely to be heterogeneous if we consider a different, larger scale (also consider the modifiable areal unit problem).

For example, within the populations that are spread across landscapes there exist pockets of low and high fertility, mortality, and population movement or migration. Sometimes events such as births or deaths are clustered. While there is variation within all sub-regions, like things do tend to coexist in similar environments (Tobler, 1970). Demographers are frequently interested in uncovering, describing, and explaining such interesting clusters. There are a variety of exploratory tools for detecting spatial heterogeneity. Moran’s I is often used as an indicator of spatial association (Anselin, 1995; Anselin, 2005).

As a very simple visual example, Figure 1 shows estimated population density (person per square kilometer) in Thailand. It should not be surprising that there are clusters of

Figure 1

high density in some places and areas that have very low density in between. As previously mentioned, spatial heterogeneity is the norm. In this case, we would not expect that people will be distributed randomly and/or homogeneously across the landscape.

Further, when demographers attempt to investigate the occurrence of certain population phenomena, they frequently are interested in factors that contribute to the occurrence of these clusters.  For example, within a single state there can be large disparities in fertility rates. Perhaps fertility rates are on average lower in urban areas than rural areas. Additionally, cultural norms may influence fertility rates, meaning that even within urban areas there can be subgroups of the population that both live near each other (ethnic enclaves) and have higher fertility than their immediate urban neighbors. In such a case, one way to deal with spatial heterogeneity in an explanatory model is to include variables that explain this heterogeneity—such as rural/urban status and cultural groups.

However, spatial heterogeneity does not just describe the distribution of events of interest across space; it can also refer to the distribution of a relationship across a landscape. In essence, what matters in social processes may not be homogeneously distributed across a landscape. Drawing from the previous example of fertility, it is possible that predictors of high fertility vary across space. For example, cultural group may have no predictive power with regard to high fertility rates in a rural setting, although it may have a high predictive power in an urban setting. In some cases, the effect of a predictor on its outcome can even change direction (e.g., negative to positive or vice versa) depending on location. A relatively recent approach to addressing this problem (and potentially spatial dependence as well) is geographically weighted regression (Fotheringham et al., 2002).

References:

  • Anselin, L. 1995. Local indicators of spatial association—LISA. Geographical Analysis 27(2): 93–115.
  • Anselin, Luc, 2005. Exploring Spatial Data with GeoDa TM : A Workbook. Geography.
  • Anselin, Luc, 2010. Thirty years of spatial econometrics. Papers in Regional Science 89(1): 3–25.
  • Fotheringham, A.S., C. Brunsdon, and M.E. Charlton. 2002. Geographically weighted regression: The analysis of spatially varying relationships. Chichester, UK: John Wiley & Sons.
  • Tobler, W.R. 1970. A computer movie simulating urban growth in the Detroit region. Economic Geography  46: 234–240.