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- Title
ON THE DIMENSIONALITY OF PSYCHOLOGICAL PROCESSES.
- Authors
Barnett, George A.; Woelfel, Joseph
- Abstract
The article presents methods of determining the proper dimensionality of a space. One method of determining the proper dimensionality of a space is the scree test. It operates as follows. Plot the absolute values of the eigenroots for each dimension of the space. Then connect these values. The proper number of underlying dimensions is determined where there is a drastic change in the slope of the curve. This quantity is the number of dimensions which lie off the line connecting the smallest root to this point and includes the largest root on the scree line. The remaining dimensions theoretically represent measurement error. Perhaps the most popular method for determining dimensionality is through the mathematician J. Kruskal's measure of stress. While the other methods discussed in this article can be applied to both metric and nonmetric scaling, the utility of Kruskal's measure is limited to nonmetric. Stress is an indicator of goodness-of-fit between the obtained solution and the measured distances. A perfect solution indicates that there is a monotonic relationship between dissimilarities and the reconstructed distances. The criterion for selecting the proper number of dimensions is a solution where a minimum dimensionality is obtained in conjunction with a low stress value.
- Subjects
DIMENSIONS; STATISTICS; EIGENVALUES; ERRORS; KRUSKAL, J.; GOODNESS-of-fit tests
- Publication
Quality & Quantity, 1979, Vol 13, Issue 3, p215
- ISSN
0033-5177
- Publication type
Article