Nonmetric Multidimensional Scaling: A Monte Carlo Study of the Basic Parameters

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Abstract
Metric determinacy of nonmetric multidimensional scaling was investigated as a function of the number of points being scaled, the amount of error in the data being scaled, and the accuracy of estimation of the Minkowski distance function parameters, dimensionality and the r-constant. It was found that nonmetric scaling may provide better models if (1) the true structure is of low dimensionality, (2) the dimensionality of recovered structure is not less than the dimensionality of the true structure, (3) degree of error is low, and (4) the degrees of freedom ratio is greater than about 2.5. It was also found that (5) accurate estimation of the Minkowski constant leads to a better model only if the dimensionality has been properly estimated.