Certain probabilistic multivariate similarity models are shown to be special cases of moment generating functions. These models, introduced in Ennis, Palen, and Mullen (1988, Journal of Mathematical Psychology, 32, 449-465), are based on Thurstonian (1927, Psychological Review, 34, 273-286), ideas about the distribution of momentary psychological magnitudes and Shepard’s (1957, Psychometricka, 22, 325-345; 1987, Science, 237, 1317-1323), proposals about the form of the similarity function. Two cases are discussed: (a) the Euclidean/Gaussian case which is a special case of the moment generating function of a quadratic form; and (b) the city-block /exponential decay case, which is a special case of the moment generating function of the sum of folded normal random variables. In both cases, computationally simple mathematical expressions are given.
This article appears as:
Ennis, D. M. and Johnson, N. L. (1993). Thurstone-Shepard similarity models as special cases of moment generating functions. Journal of Mathematical Psychology, 37(1), 104-110.
Thurstone-Shepard similarity models as special cases of moment generating functions
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