Spatial Regression Models

By Michael Ward and Kristian Gleditsch

This book illustrates the use of spatial analysis in the social sciences within a regression framework and is accessible to readers with no prior background in spatial analysis. The text covers different modeling-related topics for continuous dependent variables, including mapping data on spatial units, creating data from maps, analyzing exploratory spatial data, working with regression models that have spatially dependent regressors, and estimating regression models with spatially correlated error structures.

Using social science examples based on real data, the authors illustrate the concepts discussed, and show how to obtain and interpret relevant results. The examples are presented along with the relevant code to replicate all the analysis using the R package for statistical computing. Users can download both the data and computer code to work through all the examples found in the text. New to the Second Edition is a chapter on mapping as data exploration and its role in the research process, updates to all chapters based on substantive and methodological work, as well as software updates, and information on estimation of time-series, cross-sectional spatial models.

Book Materials

Why Space in the Social Sciences?

Outside Geography and specialized sub-fields such as Economic Geography or Geopolitics, space has traditionally not figured very prominently in standard discussions of the social sciences. As such it may not obvious to many why social scientists should be interested in spatial regression models. In this chapter we discuss some central motivations for spatial data and spatial modeling in the social sciences, drawing on salient questions and topics.

Maps as Displays of Information

This chapter examines the history of maps, and illustrates their role as a way to display information, not to get from point A to point B. We discuss different projections for world maps and more specifically we explain the ESRI shapefile format. We explore choropleth mapping of geograpically tagged information, illustrate how to use maps to aggregate spatially tagged data, and provide an overview of pointillism and cartograms as a way to display information.

Interdependence among Observations

In this chapter, we examine how insights from spatial analysis can help researchers take dependence between observations into account and deal with spatially clustered phenomena. This includes forms of social connectivities beyond networks defined purely by geographical proximity. Social can be defined in terms of transactions, legacy, heritage, and many other aspects of social, economic, and political life. We cover how to measure proximity, and how to descriptively look for spatial patterns.

Spatially Lagged Dependent Variables

In this chapter, we describe a statistical model appropriate when there is spatial clustering in the dependent and independent variables, as in the democracy and wealth example. that incorporates spatial dependence explicitly by adding a spatially lagged dependent variable y on the right hand side of the regression equation. This model goes by many different names. Anselin (1988) calls this the spatial autoregressive model, but this terminology is potentially confusing since the term autoregressive is used to denote quite different spatial models in the geostatistical literature.

Spatial Error Model

Chapter 5 examines situations in which the spatial dependence enters through the errors, rather than through the systematic component of the model. Such a model is typically called the spatial error model. We also examine an important possible extension of spatial regression models to distance concepts based on metrics other than geography in the context of the spatial error model.


In this Chapter, we outline some extensions of spatial statistical models and some of the thorny issues that spatial analysts may face.

Please also see this related work: Maximum Likelihood Methods