Aggregate item response analysis

A stochastic postulate is given for the multiple-item, successive-intervals scaling of populations. The logistic equivalent of this postulate provides an aggregate item response model in which a unidimensional submodel may be nested. This reduction provides a subtractive conjoint measurement of several items and stimuli on the same latent scale. Generalized-least-squares methods are used to estimate and test the multiple-item model, and its unidimensional reduction, on aggregate survey responses. The entire procedure is illustrated with an analysis of semantic-differential attitude data. This analysis exhibits an item selection procedure that is applicable to various social constructs.The authors dedicate this paper to the memory and contributions of Clyde Coombs.The programming and data analyses for the present paper were carried out by José Ventura of the Department of Industrial and Systems Engineering, and Jerry Meiten of the Department of Statistics, University of Florida.The study was also supported by the College of Business Administration, University of Florida, and the Faculty of Social Sciences, Hebrew University of Jerusalem.     

Setting the sales budget: An exploratory study

This article explores how the sales budget is set in a business organization. Findings from a longitudinal participant observation study revealed that the sales budget is considered of great importance to the organization as sales estimates serve as premises for planning of production and supply and new product developments. It was observed that the sales budget was based on a narrow, inner-directed perspective, almost looking away from important environmental driving forces such as competitors and customers. The findings also showed that individuals involved in the sales budgeting process behaved opportunistically, influencing the budgetary process and outcomes. Theoretical and normative implications are highlighted.     

Examining differential item functioning due to item difficulty and alternative attractiveness

A method for analyzing test item responses is proposed to examine differential item functioning (DIF) in multiple-choice items through a combination of the usual notion of DIF, for correct/incorrect responses and information about DIF contained in each of the alternatives. The proposed method uses incomplete latent class models to examine whether DIF is caused by the attractiveness of the alternatives, difficulty of the item, or both. DIF with respect to either known or unknown subgroups can be tested by a likelihood ratio test that is asymptotically distributed as a chi-square random variable.     

An automated test development of parallel tests from a seed test

Binary programming models are presented to generate parallel tests from an itembank. The parallel tests are created to match item for item an existing seed test and match user supplied taxonomic specifications. The taxonomic specifications may be either obtained from the seed test or from some other user requirement. An algorithm is presented along with computational results to indicate the overall efficiency of the process. Empirical findings based on an itembank for the Arithmetic Reasoning section of the Armed Services Vocational Aptitude Battery are given.The Office of Naval Research, Program in Cognitive Science, N00014-87-C-0696 partially supported the work of Douglas H. Jones. The Rutgers Research Resource Committee of the Graduate School of Management partially supported the work of Douglas H. Jones and Ing-Long Wu. A Thomas and Betts research fellowship partially supported the work of Ing-Long Wu. The Human Resources Laboratory, United States Air Force, partially supported the work of Ronald Armstrong. The authors benefited from conversations with Dr. Wayne Shore, Operational Technologies, San Antonio, Texas. The order of authors' names is alphabetical and denotes equal authorship.     

Influential observations in principal factor analysis

We propose a method for detecting influential observations in iterative principal factor analysis. For this purpose we derive the influence functionsI(x; LL ^T ) andI(x; ) for the common variance matrixT =LL ^T and the unique variance matrix , respectively, in the common factor decomposition =LL ^T + . A numerical example is given for illustration.The authors are grateful to Tomoyuki Tarumi and Atsuhiro Hayashi for their kind permission to use their software Seto/B for drawing Figures 1 and 2 and to anonymous reviewers for comments on the paper.     

Using item-specific instructional information in achievement modeling

The problem of detecting instructional sensitivity (item basis) in test items is considered. An illustration is given which shows that for tests with many biased items, traditional item bias detection schemes give a very poor assessment of bias. A new method is proposed instead. This method extends item response theory (IRT) by including item-specific auxiliary measurement information related to opportunity-to-learn. Item-specific variation in measurement relations across students with varying opportunity-to-learn is allowed for.This paper was presented at the 1987 AERA meeting in Washington, DC. This research was supported by grant OERI-G-86-003 from the Office of Educational Research and Improvement, Department of Education. The author thanks Michael Hollis and Chih-fen Kao for valuable research assistance, and appreciates valuable comments made by an anonymous reviewer.     

Observing responses maintained by conditional discriminative stimuli.

In a conditional discrimination procedure, pigeons' observing responses were analyzed to examine whether two color stimuli (blue or red), conditionally related to whether each of two line stimuli (vertical or horizontal) accompanied reinforcement or nonreinforcement, functioned as conditioned reinforcers. If a variable-interval (VI) 10-s requirement was fulfilled, an observing response produced onset of a color stimulus. A little later, a line stimulus was presented independently of responding, added to the color stimulus to form a compound stimulus. If 55 s elapsed with a response not having occurred either through 55 s or after the variable-interval 10-s had timed out, one of the color-line compound stimuli was presented independently of responding. To control for sensory reinforcement effects and for earlier entrance to the later link, a simple discrimination procedure also was conducted in which reinforcement was not correlated with the color stimuli but with the line stimuli only. As in the conditional discrimination, the observing response also could produce earlier presentation of blue or red. The observing response occurred more frequently during the conditional discrimination than during the simple discrimination. The results were related to different theoretical accounts of conditioned reinforcement, particularly the information hypothesis.     

A nonparametric approach for assessing latent trait unidimensionality

Assuming a nonparametric family of item response theory models, a theory-based procedure for testing the hypothesis of unidimensionality of the latent space is proposed. The asymptotic distribution of the test statistic is derived assuming unidimensionality, thereby establishing an asymptotically valid statistical test of the unidimensionality of the latent trait. Based upon a new notion of dimensionality, the test is shown to have asymptotic power 1. A 6300 trial Monte Carlo study using published item parameter estimates of widely used standardized tests indicates conservative adherence to the nominal level of significance and statistical power averaging 81 out of 100 rejections for examinee sample sizes and psychological test lengths often incurred in practice.The referees' comments were remarkably detailed and greatly enhanced the writeup and sensitized the author to certain pertinent issues. Discussions with Fritz Drasgow, Lloyd Humphreys, Dennis Jennings, Brian Junker, Robert Linn, Ratna Nandakumar, and Robin Shealy were also very useful.This research was supported by the Office of Naval Research under grant N00014-84-K-0186; NR 150-533, and by the National Science Foundation under grant DMS 85-03321.     

Reliability of test scores in nonparametric item response theory

Three methods for estimating reliability are studied within the context of nonparametric item response theory. Two were proposed originally by Mokken (1971) and a third is developed in this paper. Using a Monte Carlo strategy, these three estimation methods are compared with four classical lower bounds to reliability. Finally, recommendations are given concerning the use of these estimation methods.The authors are grateful for constructive comments from the reviewers and from Charles Lewis.     

The effect of negative stimulus presentations on observing-response rates

Theories of observing differ in predicting whether or not a signal for absence of reinforcement (S−) is capable of reinforcing observing responses. Experiments in which S− was first removed from and then restored to the procedure have yielded mixed results. The present experiments suggest that failure to control for the direct effect of presenting S− may have been responsible. Pigeons and operant procedures were used. Experiment 1 showed that presentations of S−, even when not contingent on observing, can raise the rate of an observing response that was reinforced only by presentations of a signal (S+) that accompanied a schedule of food delivery. Experiment 2 showed that this effect resulted from bursts of responding that followed offsets of S−. Experiment 3 showed that, when the presence of S− was held constant, lower rates occurred when S− was dependent on, rather than independent of, observing. These results support theories that characterize S− as incapable of reinforcing observing responses.