THURSTONE-SHEPARD SIMILARITY MODELS AS SPECIAL CASES OF MOMENT GENERATING-FUNCTIONS

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, Psychometrika,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. © 1993 Academic Press, Inc.