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Abstract:
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I develop methods to analyze spatial point patterns where there are potentially multiple marks for each location. In the Midwest, there is a strong tradition of placing yard signs to express support for candidates or issues in an election. These are realizations of marked point patterns and provide information about the spatial heterogeneity of opinions. In the motivating example, support for or against a dominating issue in a school board election was expressed either by signs for or against a bond issue or by signs for specific candidates. In yards with both bond issue signs and candidate signs, there are strong associations between the two types of data. However, many yards have only one type of sign. The observed locations of each type of sign are treated as realizations of heterogenous Poisson processes with intensity functions that depend on a latent opinion variable. I compare the efficiencies of three estimators: one that conditions on the association, a two-stage estimator, and a simultaneous estimator. Similar methods could be used to evaluate spatial patterns in species composition data where the marks are the presence/absence of multiple species.
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