Bootstrap Confidence Regions for Multidimensional Scaling Solutions


  • Earlier versions of this article were presented at the November 2010 meeting of the University of North Carolina Political Methods Group and the 2011 annual meetings of the Midwest Political Science Association. The late George Rabinowitz provided a great deal of assistance during the early stages of this project; we are very grateful for his encouragement and suggestions. We also thank Ryan Bakker and Saundra K. Schneider for their many helpful comments on various drafts of the manuscript. All replication materials, including data files, SAS commands, R scripts, and the R package mentioned in the text are available either directly from the authors or online at


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.