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Bootstrap Confidence Regions for Multidimensional Scaling Solutions
Author(s) -
Jacoby William G.,
Armstrong David A.
Publication year - 2014
Publication title -
american journal of political science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.347
H-Index - 170
eISSN - 1540-5907
pISSN - 0092-5853
DOI - 10.1111/ajps.12056
Subject(s) - multidimensional scaling , resampling , scaling , computer science , flexibility (engineering) , variety (cybernetics) , data mining , econometrics , mathematics , statistics , algorithm , artificial intelligence , machine learning , geometry
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.