A model for repeat trial product tests

A non-forced choice model is developed that describes subject behavior on repeat trial discrimination tests of the pick 1 ofk form. The model is developed from the Dirichlet distribution, and it allows for the derivation of individual true scores and of sampling properties for various constructs of interest. These results permit the analysis and comparison of test designs. The model is applied to issues such as forced vs. non-forced choice formats, the best number of alternatives at a choice point, and the selection of expert panels.     

Six-member stimulus classes generated by conditional-discrimination procedures

In conditional-discrimination procedures with three sets of stimuli, A, B, and C, three stimuli per set (A1A2A3, B1B2B3, and C1C2C3), subjects (children and adults) learned to select Set-B and Set-C comparisons conditionally upon Set-A samples (A1B1, A1C1, A2B2, A2C2, A3B3, A3C3). If the conditional-discrimination procedures also generated equivalence relations, three 3-member stimulus classes would be demonstrable, A1B1C1, A2B2C2, and A3B3C3. In addition to these three sets, the present experiments used three other sets of stimuli--D, E, and F. The subjects learned to select Set-E and Set-F comparisons conditionally upon Set-D samples (D1E1, D1F1, D2E2, D2F2, D3E3, D3F3). This established a second group of three 3-member stimulus classes, D1E1F1, D2E2F2, and D3E3F3. In all, two groups of three 3-member classes were established by teaching subjects 12 conditional discriminations. The two groups of 3-member classes were then combined (successfully for 5 of 8 subjects) into a single group of three 6-member classes by teaching the subjects three more conditional relations (E1C1, E2C2, and E3C3). With three other children, enlarging the classes one member at a time also produced 6-member classes. As a consequence of class formation, 60 untrained conditional relations emerged from 15 that had been explicitly taught. Six of the subjects also proved capable of naming the stimuli consistently in accord with their class membership, but two subjects demonstrated class formation even in the absence of consistent naming.     

Allowing for infeasible pairings in the matching paradigm

The objective of research in the matching paradigm is to determine whether a one-to-one pairing configuration between objects in two arrays contains more pairings of a particular kind than expected under the null hypothesis. The presence of infeasible pairings, that is, of particular pairings which can not possibly take place, has the effect of altering the null distribution that would otherwise obtain. To enable researchers to determine the appropriate null distribution, a generalization of classical rook methodology is developed which can accommodate infeasible pairings in the matching paradigm.     

An application of order restricted inference methodology to a problem in psychiatry

Using data which reflects upon the genetic makeup of patients, Cadoret, Woolson and Winokur (1977) test two theories regarding the genetic makeup of patients suffering from unipolar affective disorder. This hypothesis test is a good example of a problem in order restricted inference. Using some recently developed techniques in order restricted inference we analyze these data and compare the analyses.This research was sponsored by the Office of Naval Research under contract N00014-80-C-0321.     

A still further note on freeman's measure of association

This article demonstrates that Freeman's theta, a measure of association between a nominal variable and an ordinal variable, has a sampling distribution identical with the sampling distribution of Mann-Whitney'sU.     

Psychometric and information processing properties of selected response time models

This paper discusses the compatibility of some response time (RT) models with psychometric and with information processing approaches to response times. First, three psychometrically desirable properties of probabilistic models for binary data, related to the principle of specific objectivity, are adapted to the domain of RT models. One of these is the separability of item and subject parameters, and another is double monotonicity. Next, the compatibility of these psychometric properties with one very popular information processing approach, the serial-additive model, is discussed. Finally, five RT models are analyzed with respect to their compatibility with the psychometric properties, with serial-additive processing and with some alternative types of processing. It is concluded that (a) current psychometric models each satisfy one or more of the psychometric properties, but are not (easily) compatible with serial-additive processing, (b) at least one serial-additive processing model satisfies separability of item and subject parameters, and (c) RT models will more easily satisfy double monotonicity than the other two psychometric properties.     

A general model for preferential and triadic choice in terms of centralF distribution functions

A model for preferential and triadic choice is derived in terms of weighted sums of centralF distribution functions. This model is a probabilistic generalization of Coombs' (1964) unfolding model and special cases, such as the model of Zinnes and Griggs (1974), can be derived easily from it. This new form extends previous work by Mullen and Ennis (1991) and provides more insight into the same problem that they discussed.     

Asymptotic distributions of the estimators of communalities in factor analysis

Asymptotic distributions of the estimators of communalities are derived for the maximum likelihood method in factor analysis. It is shown that the common practice of equating the asymptotic standard error of the communality estimate to the unique variance estimate is correct for standardized communality but not correct for unstandardized communality. In a Monte Carlo simulation the accuracy of the normal approximation to the distributions of the estimators are assessed when the sample size is 150 or 300. This study was carried out in part under the ISM Cooperative Research Program (90-ISM-CRP-9).     

The nontruncated marginal of a truncated bivariate normal distribution

Inference is considered for the marginal distribution ofX, when (X, Y) has a truncated bivariate normal distribution. TheY variable is truncated, but only theX values are observed. The relationship of this distribution to Azzalini's skew-normal distribution is obtained. Method of moments and maximum likelihood estimation are compared for the three-parameter Azzalini distribution. Samples that are uniformative about the skewness of this distribution may occur, even for largen. Profile likelihood methods are employed to describe the uncertainty involved in parameter estimation. A sample of 87 Otis test scores is shown to be well-described by this model.     

A new interpretation of stochastic test models

A new look at latent trait models is proposed. The event of an item being solved by a person is related to the event that the momentary value of a person-specific random component is at least as large as the corresponding value of an item-specific random component. The Birnbaum logistic test model is shown to be generated by a bivariate extreme value distribution for the components. Some consequences of this interpretation are outlined.I am indebted to David Strauss for calling the extreme value distribution (1) to my attention in a random utility context. The paper also benefited from discussions with H. C. Micko, H. H. Schulze and K. F. Wender.