## Abstract

Three ideas are basic to generative theory: (a) Subjects are assumed to attend to the relations among stimuli, extracting the transformations relating pairs of stimuli; (b) the set of abstracted transformations is decomposed or reduced to an elementary set of generators; (c) subjects use the elementary generators as the basis for judging similarity. The purpose of this paper is to illustrate these ideas with an experiment in which subjects were asked to rate the similarity between stimulus pairs. The stimulus materials consisted of the permutations of a 4-item pattern with the properties of a dihedral group which insured the existence of sets of elementary transformations. Three analytic techniques were used to determine the generator set of transformations abstracted by subjects. The first analysis consisted of a monotonic regression between dissimilarity ratings and the number of elementary generators of a given permutation. The residual variance of this monotone regression, suitably normalized, was used as a quantitative goodness-of-fit measure. For the stochastic analysis, cumulative distributions of dissimilarity ratings were obtained for permutations requiring one, two, or three generators. The idea was that permutations requiring fewer generators should be associated with distributions of lower dissimilarity values (higher similarity scores) as compared to permutations predicted to be transformationally more complex. The final analysis, a multidimensional scaling of dissimilarity ratings, converted subjects' ratings into spatial structures to determine whether individual subjects' ratings exhibited the predicted spatial arrangement. The monotone regression and stochastic analyses abstracted similar generator sets for individual subjects, some of which provided perfect fits to the data. Although the scaling analysis yielded similar estimates of generators, for some subjects, transformations with the same number of generators yielded unequal "cognitive" distances resulting in some-what deformed spatial structures for these subjects. It was concluded that the results generally supported a generative model as an approximation to subjects' representations of interstimulus relationships.

Original language | English (US) |
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Pages (from-to) | 219-246 |

Number of pages | 28 |

Journal | Journal of Mathematical Psychology |

Volume | 21 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1980 |

### Bibliographical note

Funding Information:i This article is based on a thesis submitted by the first author in partial fulfillment for the Ph.D. degree at the University of Minnesota. The thesis work was developed further while the first author held a Post Doctoral Fellowship from the National Institutes of Health (Grant MH-00235) and in part by a grant to Richard Millward from the National Science Foundation (Grant NSF GB 34122-Al). A portion of this research was presented by the first author at the Society of Mathematical Psychology Hamilton, Ontario, August 1978. Requests for reprints should be sent to Willa Kay Wiener-Ehrlich c/o Dr. Richard Millward, Department of Psychology, Brown University, Providence, R.I. 02912.