Spatial and conjoint models based on pairwise comparisons of dissimilarities and combined effects: Complete and incomplete designs

In pairwise multidimensional scaling, a spatial representation for a set of objects is determined from comparisons of the dissimilarity of any two objects drawn from the set to the dissimilarity of other pairs of objects drawn from that set. In pairwise conjoint scaling, comparisons among the joint effects produced by pairs of objects, where the objects in a pair are drawn from separate sets, are used to determine numerical representations for the objects in each set. Monte Carlo simulations of both pairwise dissimilarities and pairwise conjoint effects show that Johnson's algorithm can provide good metric recovery in the presence of high levels of error even when only a small percentage of the complete set of pairwise comparisons are tested.

[1]  Equal loudness contours derived from comparisons of sensory differences. , 1987, Canadian journal of psychology.

[2]  A. Tversky,et al.  Foundations of Measurement, Vol. I: Additive and Polynomial Representations , 1991 .

[3]  W. Levelt,et al.  Binaural additivity of loudness. , 1972, The British journal of mathematical and statistical psychology.

[4]  B. Schneider,et al.  The dimensions of tonal experience: A nonmetric multidimensional scaling approach , 1981, Perception & psychophysics.

[5]  Conjoint scaling of the utility of money using paired comparisons , 1988 .

[6]  R. M. Johnson,et al.  A simple method for pairwise monotone regression , 1975 .

[7]  Forrest W. Young Nonmetric multidimensional scaling: Recovery of metric information , 1970 .

[8]  R. Luce,et al.  Simultaneous conjoint measurement: A new type of fundamental measurement , 1964 .

[9]  Bruce A. Schneider,et al.  A technique for the nonmetric analysis of paired comparisons of psychological intervals , 1980 .

[10]  Jaap Van Brakel,et al.  Foundations of measurement , 1983 .

[11]  Scott Parker,et al.  The measurement of loudness using direct comparisons of sensory intervals. , 1974 .

[12]  S. Schiffman Introduction to Multidimensional Scaling , 1981 .

[13]  I. Spence,et al.  Single subject incomplete designs for nonmetric multidimensional scaling , 1974 .

[14]  B. Schneider,et al.  Individual loudness functions determined from direct comparisons of loudness intervals , 1980, Perception & psychophysics.

[15]  R. M. Johnson,et al.  Pairwise nonmetric multidimensional scaling , 1973 .

[16]  B. Schneider The additivity of loudness across critical bands: A conjoint measurement approach , 1988, Perception & psychophysics.

[17]  A note on the nonmetric analysis of psychological intervals for an unknown ordering of stimuli , 1983 .