I've performed couple of multidimensional scaling analysis for the items of the Mathematical Problems questionnaire used as a subtest in the JCCES. I was looking for the one-dimensionality to be shown by variables' coordinates in two-dimensional Euclidian distances and a generated Guttman effect (1955): the so-called horseshoe shape. However, I had to try different measurement levels in order to achieve such phenomenon. Although both the nominal and the ordinal levels produced a shy half-circle (which indeed has an interpretative interest), the figure wasn't satisfactory with a grape of items in the middle. Finally, the horseshoe appeared in a clearer aspect with the use the ratio measurement level.
According to Steven (1951), the ratio-scale is an interval-scale with a rational origin. The interval-scale provides with relative relationships between points and the ratio-scale shows the determinate distances from a fixed origin.
References.
Guttman, L (1955). A generalized simplex for factor analysis. Psychometrika, 20, pp 173-192.
Stevens, S. S. (1951). Mathematics, measurement and psychophysics. In S. S. Stevens (Ed.), Handbook of experimental psychology (pp. 1-49). New York: Wiley.
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