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.     

A method of optimal scaling for multivariate ordinal data and its extensions

This paper develops a method of optimal scaling for multivariate ordinal data, in the framework of a generalized principal component analysis. This method yields a multidimensional configuration of items, a unidimensional scale of category weights for each item and, optionally, a multidimensional configuration of subjects. The computation is performed by alternately solving an eigenvalue problem and executing a quasi-Newton projection method. The algorithm is extended for analysis of data with mixed measurement levels or for analysis with a combined weighting of items. Numerical examples and simulations are provided. The algorithm is discussed and compared with some related methods.Earlier results of this research appeared in Saito and Otsu (1983). The authors would like to acknowledge the helpful comments and encouragement of the editor.     

The autoshaping procedure as a residual block clock

In the first experiment, 4 pigeons were each presented with a recurring sequence of four key colors followed by the delivery of grain (block clock). Once the rate of pecking had stabilized, three of the colors were replaced, during different series of sessions, by a darkening of the key. The rate of pecking was reduced within those segments of the interval between deliveries of food during which the key was dark; when the key was dark during the final portion of the interval, rates were reduced throughout the entire interval. In the second experiment, 3 new pigeons were exposed to a different sequence of colors, and the final stimulus was replaced in successive conditions by a novel color, a darkened key, and a restoration of the original color. The data indicated that darkening the key had a more severe, more extensive, and more persistent effect than did a mere change in color. These results suggest that it may be fruitful to conceptualize the autoshaping procedure as a special version of the block clock in which pecking is suppressed throughout the greater part of the interval by darkening the key. In the final condition, the same stimulus appeared in each of the last three portions of the interval. The rate of pecking was lower during the last two portions than when distinctive colors were presented, with the peak rate now appearing in the fifth of seven equal temporal components.     

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.     

Criterion-related construct validity

Established results on latent variable models are applied to the study of the validity of a psychological test. When the test predicts a criterion by measuring a unidimensional latent construct, not only must the total score predict the criterion, but the joint distribution of criterion scores and item responses must exhibit a certain pattern. The presence of this population pattern may be tested with sample data using the stratified Wilcoxon rank sum test. Often, criterion information is available only for selected examinees, for instance, those who are admitted or hired. Three cases are discussed: (i) selection at random, (ii) selection based on the current test, and (iii) selection based on other measures of the latent construct. Discriminant validity is also discussed.This work was supported in part by Grant SES-87-01890 from the Measurement Methods and Data Improvement Program of the U.S. National Science Foundation.     

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.     

Children's choice: Sensitivity to changes in reinforcer density

Two experiments were carried out in which children's sensitivity to changes in reinforcer density (number of reinforcers per session) was measured in a choice paradigm. In Experiment 1, 24 girls (ages 6, 9, and 12 years) performed on concurrent-chain schedules of reinforcement. The initial links were variable-interval 10-s schedules. One terminal link always gave three tokens after 30 s, but the parameters associated with the other were varied. Independent manipulations of reinforcer size (two tokens or four tokens) and prereinforcement delay (25 s or 65 s) led to equal changes in the relative density of tokens that could be earned on the schedules. Subjects at all ages were sensitive to changes in reinforcer density brought about by changes in reinforcer size, whereas only 3 12-year-olds showed sensitivity to the changes brought about by manipulation of prereinforcer delay. In Experiment 2, titration procedures were used to test the extent of this insensitivity to delay in 32 6- and 12-year-old children. In these procedures, a repeated choice of the large reinforcer increased the delay to its delivery, and a repeated choice of the small reinforcer reduced the delay to the delivery of the large reinforcer. Whereas 6-year-old boys and girls tended to maintain a strong preference for the large reinforcer, so increasing the delay to its delivery, 12-year-olds tended to distribute their responses to both alternatives, thus producing a stable level of delay to the large reinforcer. The results from the two experiments support the idea of two stages in the development of adaptive intertemporal choice.     

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.