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Bootstrap Confidence Regions for Multidimensional Scaling Solutions

William G. Jacoby Michigan State University David A. Armstrong II University of Wisconsin–Milwaukee

Multidimensional scaling (or MDS) is a methodology for producing geometric models of proximities data. Multidimensional scaling has a long history in political science research. However, most applications of MDS are purely descriptive, with no attempt to assess stability or sampling variability in the scaling solution. In this article, we develop a bootstrap resampling strategy for constructing confidence regions in multidimensional scaling solutions. The methodology is illustrated by performing an inferential multidimensional scaling analysis on data from the 2004 American National Election Study (ANES). The bootstrap procedure is very simple, and it is adaptable to a wide variety of MDS models. Our approach enhances the utility of multidimensional scaling as a tool for testing substantive theories while still retaining the flexibility in assumptions, model details, and estimation procedures that make MDS so useful for exploring structure in data.

he term “multidimensional scaling” (usually abbreviated “MDS”) refers to a general methodology for producing a geometric model of proximities data.1 Multidimensional scaling has a long history in political science. However, almost all applications have been descriptive in nature; there have been few attempts to assess the stability of MDS models or to generate inferences about a population structure from a scaling solution that is based upon observed sample data. In this article, we develop a bootstrap resampling strategy for constructing confidence regions in multidimensional scaling solutions. Our procedure is very simple, it is adaptable to a wide variety of MDS models, and it overcomes some of the limitations associated with earlier attempts to assess statistical stability in multidimensional scaling solutions. This is important because the...