Construction of Maps from “Odd Bits of Information”

Multidimensional Scaling of Binary Dissimilarities: Direct and Derived Approaches

Given a matrix of dissimilarities, it has been debated whether researchers should perform multidimensional scaling on this original matrix or on a new one derived by comparing rows in the original matrix. Careful comparison studies (Drasgow & Jones, 1979; Van der Kloot & Van Herk, 1991) in the context of sorting data indicated that most of the initial enthusiasm for the derivative approach was unfounded. The current work, a Monte Carlo study of structured binary data derived from known two-dimensional configurations using ALSCAL, complements and extends the previous studies. We discuss a weakness in the squared difference (δ) row-comparison rule used previously and propose an alternative row-comparison measure based on the Jaccard coefficient. Scaling the binary data directly gave better performance, as gauged by Procrustes statistics, than did scaling A data across a range of noise levels. The quality of solutions obtained by scaling Jaccard data was always better or essentially equal to that from scaling δ data, and in certain parameter regions improved upon that of direct scaling. Another alternative approach, applying the δ rule after first row-centering the binary data, was found to be generally ineffective. These findings are pertinent to the analysis not just of stimulus sorting data but of coarse dissimilarities generally, for example from direct pairwise judgment tasks and in fields outside statistical psychology.

The application of multidimensional scaling methods to epidemiological data

This paper illustrates the use of multidimensional scaling methods (MDS) to examine space-time patterns in epidemic data. The paper begins by outlining the principles of MDS. The model is then formally specified and illustrated by application to two data sets. The first is partly a tutorial example. It uses monthly reported measles morbidity data for the 31-year period from January 1960 to December 1990, collected for the 50 states of the USA, plus New York City and the District of Columbia. These data are used to explore the various ways in which MDS may be used to identify changing spatial patterns in geographically-coded data. In addition to their tutorial use, the data are also employed to search for any substantive changes in the geographical structure of measles epidemics in the USA that may have followed the introduction of mass vaccination in 1965. New England appears to have developed an epidemic profile distinct from the rest of the USA, and there is tentative evidence of an urban-rural split in epidemic characteristics. The second data set takes annual reported measles mortality data for New Zealand and the states of Australia from 1860 to 1949. MDS is used to show how the spatial relationships among these geographical units have changed over time in response to changes in the sizes of local susceptible populations.