A generalization of the Yule-Simon model,with special reference to word association tests and neural cell assembly formation

A generalization of the Yule-Simon model is suggested and such related questions as inversion problems and nonequilibrium behavior are solved. The generalization follows the work of Haight and Jones (Journal of Mathematical Psychology, 1974, 11, 237–244) and thus special reference is made to word association tests. Some new possible applications of the presented model are offered, namely, in the field of neural cell assemblies.     

A dynamic generalization of the Rasch model

In the present paper a model for describing dynamic processes is constructed by combining the common Rasch model with the concept of structurally incomplete designs. This is accomplished by mapping each item on a collection of virtual items, one of which is assumed to be presented to the respondent dependent on the preceding responses and/or the feedback obtained. It is shown that, in the case of subject control, no unique conditional maximum likelihood (CML) estimates exist, whereas marginal maximum likelihood (MML) proves a suitable estimation procedure. A hierarchical family of dynamic models is presented, and it is shown how to test special cases against more general ones. Furthermore, it is shown that the model presented is a generalization of a class of mathematical learning models, known as Luce's beta-model.     

A generalization of the interpoint distance model

Coombs and Kao have conjectured that, given the distances between a set of points representing persons and another representing objects, factor analytic methods can be used to recover the locations of the persons and objects. In the present paper it is proved that the conjecture applies, with some qualifications, to squared distances rather than distances themselves. Possible applications to scaling and to inventory responses are discussed.Most of the work that resulted in this paper was done while the authors were affiliated with Educational Testing Service. Portions of this paper were presented at the APA convention, St. Louis, 1962.     

Comparisons of power for some exact multinomial significance tests

Two small-sample tests (proposed by Tate and Clelland and by Chapanis respectively) of hypotheses about the parameters of the multinomial distribution, where

$$f(x|p) = n!\prod\limits_{i = 1}^k {\frac{{p_i^{x_i } }}{{x_i !}}} $$     

A note on keats' generalization of the rasch model

An alternative derivation is given for a simple test model which incorporates anability parameter for the subject anddifficulty level andguessing parameters for the problem. The probability of a correct response to the problem is a projective transformation of the problem difficulty. The ability and difficulty parameters separate into additive components.     

Stimulus generalization: some predictions from a model of Pavlovian conditioning.

Three experiments examined predictions generated by incorporating a common-elements account of stimulus generalization within the Rescorla-Wagner model of conditioning. All experiments employed rats in a conditioned suppression situation. Experiments 1 and 2 found that conditioning of a similar stimulus augmented the excitation controlled by a near-asymptotic target stimulus more than did further conditioning of the target itself. Prior discrimination training between the target and the similar stimulus enlarged this effect, compared with prior discrimination between the target and another dissimilar stimulus. Nonreinforced exposure of the similar stimulus prior to its reinforcement also increased the effect. Experiment 3 examined a related prediction for inhibition. After discrimination training, extinction of the previously reinforced stimulus revealed more inhibition to the previously nonreinforced stimulus when those two stimuli were more similar. These outcomes are consistent with deductions from the present model and encourage further testing of its expansion to the case of stimulus generalization.     

The derivation of some tests for the rasch model from the multinomial distribution

The present paper is concerned with testing the fit of the Rasch model. It is shown that this can be achieved by constructing functions of the data, on which model tests can be based that have power against specific model violations. It is shown that the asymptotic distribution of these tests can be derived by using the theoretical framework of testing model fit in general multinomial and product-multinomial models. The model tests are presented in two versions: one that can be used in the context of marginal maximum likelihood estimation and one that can be applied in the context of conditional maximum likelihood estimation.I am indebted to Norman Verhelst and Niels Veldhuijzen for their helpful comments. Requests for reprints should be sent to Cees A. W. Glas, Cito, PO Box 1034, 6801 MG Arnhem, THE NETHERLANDS.     

Perceptual classes established with forced-choice primary generalization tests and transfer of function

In Experiment 1, 20 college students learned two identity conditional discriminations using squares that differed in interior-fill percentage (called Fill23 and Fill77). A two-choice generalization test was then presented with number of test trials varied across groups of subjects. The test samples were 19 squares that ranged in fill value from 23% to 77%; the comparisons were squares with Fill23 and Fill77. The resulting gradients did not vary as a function of number of test trials. When the generalization test was repeated with a third comparison, "neither," the ranges of fill values that occasioned the exclusive selection of Fill23 or Fill77 were direct functions of the number of prior two-choice generalization trials. Finally, a disriminability test revealed that Fill23 and Fill77 were disciminable from the intermediate fill values. In Experiment 2, perceptual classes were established with 5 new students using 760 forced-choice generalization test trials. The student were then trained to select a different glyph in the presence of Fill23 and Fill77, followed by a three-choice generalization test in which the 19 fill stimuli served as samples and the two glyphs served as comparisons. The gradients ovelapped with those previously obtained during the three-choice generalization test that used Fill23 and Fill77 as comparisons. Finally, a discriminability test showed that many adjacent stimuli along thc fill dimension were discriminable from each other. Together, the results of both experiments suggest that ranges of fill-based stimuli functioned as members of perceptual classes, and each class also functioned as a transfer network for a new selection-based response.     

On Keats' generalization of the rasch model

Parameter estimation for Keats generalization of the Rasch model that takes account of guessing behavior is investigated. It is shown that no minimal sufficient statistics for the ability parameters independent of the difficulty parameters exist. Thus Andersen's conditional inference technique for consistent estimation is not applicable to Keats' model. The notion of separability of the parameters is generalized.     

Stimulus and response generalization: A stochastic model relating generalization to distance in psychological space

A mathematical model is developed in an attempt to relate errors in multiple stimulus-response situations to psychological inter-stimulus and inter response distances. The fundamental assumptions are (a) that the stimulus and response confusions go on independently of each other, (b) that the probability of a stimulus confusion is an exponential decay function of the psychological distance between the stimuli, and (c) that the probability of a response confusion is an exponential decay function of the psychological distance between the responses. The problem of the operational definition of psychological distance is considered in some detail.This paper is based upon the theoretical sections of a Ph.D. dissertation submitted to the Graduate School of Yale University and upon subsequent modification carried out on a National Academy of Sciences-National Research Council Postdoctoral Associateship at the Naval Research Laboratory. The author is particularly indebted to Drs. C. I. Hovland, R. P. Abelson, and B. S. Rosner for their generous advice and support. Helpful criticisms have also been contributed by Drs. G. A. Miller, F. A. Logan, W. D. Garvey, J. G. Holland, and H. Glaser.