A multidimensional theory of similarity on which the mental representations of stimulus objects are assumes to be drawn from multivariate normal distributions is described. A distance-based similarity function is defined and the expected value of similarity is derived. This theory is the basis for a possible explanation of paradoxical results with highly similar stimuli regarding the form of the similarity function and the distance metric. A stochastic approach to multidimensional scaling based on same-different judgments is demonstrated using artificial and real data sets. The theory of similarity presented is used as a basis for a Thurstonian extension of Shepard’s model of identification performance.
This article appears as:
Ennis, D. M., Palen, J. and Mullen, K. (1988). A multidimensional stochastic theory of similarity. Journal of Mathematical Psychology, 32(4), 449-465.
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A multidimensional stochastic theory of similarity
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