A Multidimensional Scaling Model for the Size-Weight Illusion
- 1 March 1982
- journal article
- Published by Cambridge University Press (CUP) in Psychometrika
- Vol. 47 (1) , 25-45
- https://doi.org/10.1007/bf02293849
Abstract
The kinds of individual differences in perceptions permitted by the weighted euclidean model for multidimensional scaling (e.g., INDSCAL) are much more restricted than those allowed by Tucker’s Three-mode Multidimensional Scaling (TMMDS) model or Carroll’s Idiosyncratic Scaling (IDIOSCAL) model. Although, in some situations the more general models would seem desirable, investigators have been reluctant to use them because they are subject to transformational indeterminacies which complicate interpretation. In this article, we show how these indeterminacies can be removed by constructing specific models of the phenomenon under investigation. As an example of this approach, a model of the size-weight illusion is developed and applied to data from two experiments, with highly meaningful results. The same data are also analyzed using INDSCAL. Of the two solutions, only the one obtained by using the size-weight model allows examination of individual differences in the strength of the illusion; INDSCAL can not represent such differences. In this sample, however, individual differences in illusion strength turn out to be minor. Hence the INDSCAL solution, while less informative than the size-weight solution, is nonetheless easily interpretable.Keywords
This publication has 22 references indexed in Scilit:
- Candelinc: A General Approach to Multidimensional Analysis of Many-Way Arrays with Linear Constraints on ParametersPsychometrika, 1980
- Transformation of a Three-Mode Multidimensional Scaling Solution to Indscal FormPsychometrika, 1976
- More Factors than Subjects, Tests and Treatments: An Indeterminacy Theorem for Canonical Decomposition and Individual differences ScalingPsychometrika, 1976
- Effects on Indscal of Non-Orthogonal Perceptions of Object Space DimensionsPsychometrika, 1976
- Relations between Multidimensional Scaling and Three-Mode Factor AnalysisPsychometrika, 1972
- Multidimensional Scaling: Combining Observations when Individuals have Different Perceptual StructuresPsychometrika, 1969
- INDIVIDUAL DIFFERENCES IN MULTIDIMENSIONAL SCALING*ETS Research Bulletin Series, 1968
- A Remark on Tucker and Messick's “Points of View” AnalysisPsychometrika, 1966
- An Individual differences Model for Multidimensional ScalingPsychometrika, 1963
- The approximation of one matrix by another of lower rankPsychometrika, 1936