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.     

Initial hospitalization and community tenure outcomes of intensive case management for children and youth with serious emotional disturbance

Since 1988 New York State's Children and Youth Intensive Camse Management (CYICM) program has enrolled more than 1,700 children. The program goal is to maintain children in the least restrictive environment approriate to their needs. This linkagke and advocacy focussed program uses a small caseload and flexible service money to meet its goal. We review the program model, describe the enrolled children, highlight some of the problems associated with determining program outcomes, and present the outcomes related to hospitalization and community tenure. Using two analytic techniques, CYICM was shown to be associated with fewer hospital admissions and fewer days in the hospital over a two-year period following the intervention of CYICM than prior to enrollment.     

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.     

The comparison of interdependent correlations between optimal linear composites

A general procedure is provided for comparing correlation coefficients between optimal linear composites. The procedure allows computationally efficient significance tests on independent or dependent multiple correlations, partial correlations, and canonical correlations, with or without the assumption of multivariate normality. Evidence from some Monte Carlo studies on the effectiveness of the methods is also provided.This research was supported in part by an operating grant (#67-4640) to the first author from the National Sciences and Engineering Research Council of Canada. The authors would also like to acknowledge the helpful comments and encouragement of Alexander Shapiro, Stanley Nash, and Ingram Olkin.     

The effect of reinforcement differences on choice and response distribution during stimulus compounding

In Experiments I and II, rats were trained to respond on one lever during light and another during tone. The absence of tone and light controlled response cessation. In the multiple schedule of Experiment I, all reinforcements were received for responding in tone or light; in the chain schedule of Experiment II, all reinforcements were received in no tone + no light for not responding. Experiment I subjects, for which tone and light were associated with response and reinforcement increase, responded significantly more to tone-plus-light than to tone or light alone (additive summation). Experiment II subjects, for which tone and light were associated with response increase and reinforcement decrease, responded comparably to tone, light, and tone + light. Thus, additive summation was observed when stimulus-response and stimulus-reinforcer associations in tone and light were both positive, but not when they were conflicting. All subjects in both experiments responded predominantly on the light-correlated lever during tone + light, even when light intensity was reduced in testing. Furthermore, when a light was presented to a subject engaged in tone-associated responding, all subjects immediately switched the locus of responding to the light-correlated lever. No change in locus occurred when a tone was presented to a subject engaged in light-associated responding, irrespective of the stimulus-reinforcer association conditioned to tone. The light-lever preference in tone + light indicates that the heightened responding observed in Experiment I was not the summation of tone-associated behavior with light-associated behavior. Rather, it appears to be the result of a facilitation of one operant (light-associated responding) by the reinforcement-associated cue for the other.     

Observed-score equating as a test assembly problem

A set of linear conditions on item response functions is derived that guarantees identical observed-score distributions on two test forms. The conditions can be added as constraints to a linear programming model for test assembly that assembles a new test form to have an observed-score distribution optimally equated to the distribution on an old form. For a well-designed item pool and items fitting the IRT model, use of the model results into observed-score pre-equating and prevents the necessity ofpost hoc equating by a conventional observed-score equating method. An empirical example illustrates the use of the model for an item pool from the Law School Admission Test.The authors are most indebted to Norman D. Verhelst for suggesting Proposition 4 and its proof, to the Law School Admission Council (LSAC) for making available the data set, and to Wim M. M. Tielen for his computational assistance.