Recently in this journal, Gary Cox introduced a special issue by noting that “The spatial model is the workhorse theory of modern legislative studies” (Cox 2001, p. 189). In this special issue, the focus is on a different type of spatial model than that typically used in legislative studies. Specifically, we concentrate on models in which the data are dependent on one another as a result of geographic influences, broadly defined.

For more than half a century, social scientists have probed the aggregate correlates of the vote for the Nazi party (NSDAP) in Weimar Germany. Since individual-level data are not available for this time period, aggregate census data for small geographic units have been heavily used to infer the support of the Nazi party by various compositional groups. Many of these studies hint at a complex geographic patterning. Recent developments in geographic methodologies, based on Geographic Information Science (GIS) and spatial statistics, allow a deeper probing of these regional and local contextual elements. In this paper, a suite of geographic methods—global and local measures of spatial autocorrelation, variography, distance-based correlation, directional spatial correlograms, vector mapping, and barrier definition (wombling)—are used in an exploratory spatial data analysis of the NSDAP vote. The support for the NSDAP by Protestant voters (estimated using King's ecological inference procedure) is the key correlate examined. The results from the various methods are consistent in showing a voting surface of great complexity, with many local clusters that differ from the regional trend. The Weimar German electoral map does not show much evidence of a nationalized electorate, but is better characterized as a mosaic of support for “milieu parties,” mixed across class and other social lines, and defined by a strong attachment to local traditions, beliefs, and practices.

This article demonstrates how spatially dependent data with a categorical response variable can be addressed in a statistical model. We introduce the idea of an autologistic model where the response for one observation is dependent on the value of the response among adjacent observations. The autologistic model has likelihood function that is mathematically intractable, since the observations are conditionally dependent upon one another. We review alternative techniques for estimating this model, with special emphasis on recent advances using Markov chain Monte Carlo (MCMC) techniques. We evaluate a highly simplified autologistic model of conflict where the likelihood of war involvement for each nation is conditional on the war involvement of proximate states. We estimate this autologistic model for a single year (1988) via maximum pseudolikelihood and MCMC maximum likelihood methods. Our results indicate that the autologistic model fits the data much better than an unconditional model and that the MCMC estimates generally dominate the pseudolikelihood estimates. The autologistic model generates predicted probabilities greater than 0.5 and has relatively good predictive abilities in an out-of-sample forecast for the subsequent decade (1989 to 1998), correctly identifying not only ongoing conflicts, but also new ones.

A continuing tradition in contextual analysis locates individual citizens within spatially defined, aggregate settings in an effort to provide a more complete account of individual behavior. Given the increasing individual mobility within society, it is less than clear that geography continues to define the boundaries on meaningful aggregate contexts—people have become less tied to their geographic contexts, and technology makes it possible for citizens to maintain relationships independently of space, distance, and location. In this paper we pursue an analysis and set of analytic techniques that are designed to connect individual voters, their communication networks, and the geography that surrounds them. The analytic techniques utilize a unique data set that captures spatial dispersion in an individual's social and political network, and from these analyses we can draw two conclusions. First, spatial dispersion in a network does have an effect on interaction within the network; the world is not full of voters who operate independently of their geographic contexts. Second, spatial dispersion provides opportunities to connect citizens living in different geographic contexts, thereby creating bridges for communication across different contexts. These findings suggest that scholars might profitably incorporate geography as an important component of the complex relationships among and between individual citizens in explaining the role of the individual in modern democratic politics.

This paper examines the role of spatial effects in ecological inference. Both formally and through simulation experiments, we consider the problems associated with ecological inference and cross-level inference methods in the presence of increasing degrees of spatial autocorrelation. Past assessments of spatial autocorrelation in aggregate data analysis focused on unidimensional, one-directional processes that are not representative of the full complexities caused by spatial autocorrelation. Our analysis is more complete and representative of true forms of spatial autocorrelation and pays particular attention to the specification of spatial autocorrelation in models with random coefficient variation. Our assessment focuses on the effects of this specification on the bias and precision of parameter estimates.

Few better ways of checking and improving statistical methods exist than having other researchers go over your results, and so I especially appreciate the efforts in Anselin and Cho (2002), hereinafter AC. In this note, I make two main points.

We read with interest the sundry points raised by King in his comment (2002) on our article (Anselin and Cho 2002). Given the space and time constraints in this forum, it is impossible for us to address adequately all of the issues here. It is sufficient to say that we strongly disagree with King's claims that we are “missing the point.” We will pursue a more thorough and formal rebuttal elsewhere, but would like to set the record straight on a few issues in the limited space provided here.

We show that temporal, spatial, and dyadic dependencies among observations complicate the estimation of covariance structures in panel databases. Ignoring these dependencies results in covariance estimates that are often too small and inferences that may be more confident about empirical patterns than is justified by the data. In this article, we detail the development of a nonparametric approach, window subseries empirical variance estimators (WSEV), that can more fully capture the impact of these dependencies on the covariance structure. We illustrate this approach in a simulation as well as with a statistical model of international conflict similar to many applications in the international relations literature.