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- Title
A Note on the Multidimensional Scaling of Conditional Proximity Data.
- Authors
Green, Paul E.; Maheshwari, Arun
- Abstract
In summary, the Monte Carlo analysis has demonstrated that good recovery of artificially generated configurations is possible from the rank order of conditional proximities alone, at least in cases where the number of points (n = 15 in this case) is large relative to the dimensionality of the configuration." From an experimental standpoint, there appears to be little choice between the triangularization versus unfolding methods. (In real applications, however, it would seem that the triangularization procedure might be less susceptible to local minimum problems when arbitrary starting configurations are used in the Kruskal program.) This general finding suggests that procedures like n-dimensional rank order, which for large n require substantially fewer comparisons than tetrad procedures, could still provide enough constraints to lead to "determinate" metric solutions. Of additional interest is the relative insensitivity of configuration recovery to "ties" in the data. This suggests that in real applications the effect of inattention or fatigue on configuration "recovery" may be less than we had imagined prior to running the simulation. This finding appears relevant for either tetrad or n-dimensional rank order data collection. Finally, both findings provide some support for the robustness of nonmetric procedures under conditions where the total number of constraints remains large relative to the number of coordinate values necessary to specify the configuration. These results, while limited to synthetic data, should be somewhat reassuring to researchers interested in applying nonmetric scaling techniques to field-level data.
- Subjects
PROXIMITY matrices; MULTIDIMENSIONAL scaling; MATHEMATICAL models of industrial management; ORDINAL measurement; TRIANGULARIZATION (Mathematics); ESTIMATION theory; MATHEMATICAL models in business; PSYCHOMETRICS; MONTE Carlo method; SCALING (Social sciences)
- Publication
Journal of Marketing Research (JMR), 1970, Vol 7, Issue 1, p106
- ISSN
0022-2437
- Publication type
Article
- DOI
10.2307/3149517