Nested Analysis with Spatially Dependent Data: Sequencing Large-N and Small-N Methods

Mixed-methods designs have become increasingly popular in recent years since they promise to combine the advantages of quantitative and qualitative tools within one unified framework. Lieberman (2005) offers guidelines for case selection in “nested analysis”, where cases for the small-N analysis (SNA) are selected from a larger sample studied econometrically. Yet, since the large-N analysis (LNA) in this approach assumes that units are independently distributed, such designs are unable to account for the spatial dependence of data. In explaining an outcome of interest, dependence is seen solely as a threat to inference, rather than an issue of substantive interest. This is unfortunate, since a number of research programs in political science have recently drawn attention to diffusion, contagion and the connectedness of processes in space more broadly. Within a traditional nested analysis, the LNA is unable to account for this dependence, and if process tracing during the SNA discovers diffusion or spillover as relevant causal mechanisms, the LNA is disconnected from the SNA. This paper extends Lieberman’s “nested analysis” to spatially dependent data. We outline several strategies for what we label “geo-nested analysis” – where case selection for SNA is explicitly based on diagnostics of a previously executed spatial-econometric analysis. Specifically, we propose five techniques for case selection based on (1) spatial residual analysis, (2) cluster analysis, (3) locally-varying coefficients for predictors of interest, (4) locally-varying coefficients for the lagged error structure, and (5) locally-varying coefficients for the lagged outcome of interest. We illustrate the implications of these strategies and the conditions under which they offer most analytic leverage on the basis of data from a seminal study of homicide rates in the United States (Baller et al., 2001).