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.     

Latent trait models and dichotomization of graded responses

This paper discusses thecompatibility of the polychotomous Rasch model with dichotomization of the response continuum. It is argued that in the case of graded responses, the response categories presented to the subject are essentially an arbitrary polychotomization of the response continuum, ranging for example from total rejection or disagreement to total acceptance or agreement of an item or statement. Because of this arbitrariness, the measurement outcome should be independent of the specific polychotomization applied, for example, presenting a specific multicategory response format should not affect the measurement outcome. When such is the case, the original polychotomous model is called compatible with dichotomization.A distinction is made between polychotomization or dichotomization before the fact, that is, in constructing the response format, and polycho- or dichotomization after the fact, for example in dichotomizing existing graded response data.It is shown that, at least in case of dichotomization after-the-fact, the polychotomous Rasch model is not compatible with dichotomization, unless a rather special condition of the model parameters is met. Insofar as it may be argued that dichotomization before the fact is not essentially different from dichotomization after the fact, the value of the unidimensional polychotomous Rasch model is consequently questionable. The impact of our conclusion on related models is also discussed.     

A taxonomy of item response models

A number of models for categorical item response data have been proposed in recent years. The models appear to be quite different. However, they may usefully be organized as members of only three distinct classes, within which the models are distinguished only by assumptions and constraints on their parameters. “Difference models” are appropriate for ordered responses, “divide-by-total” models may be used for either ordered or nominal responses, and “left-side added” models are used for multiple-choice responses with guessing. The details of the taxonomy and the models are described in this paper. The present study was supported in part by two postdoctoral fellowships awarded to Lynne Steinberg: an Educational Testing Service Postdoctoral Fellowship at ETS, Princeton, NJ and an NIMH Individual National Research Service Award at Stanford University, Stanford, CA. Helpful comments by the editor and three anonymous reviewers are gratefully acknowledged.     

A temporal limit on the effect of future food on current performance in an analogue of foraging and welfare

Rats obtained access to food twice each 24-hour period. The first session was a work session in which food was available on a progressive-ratio schedule. During the second session, which occurred between 1 and 23 hours after the work session, food was freely available up to a fixed total intake each 24 hours. The situation resembled elements of several real world circumstances, including the choice between continuing to forage in a rapidly depleting patch and waiting for a better patch, and between working now and receiving a guaranteed income later. The purpose of the experiment was to explore the time period over which future access to reward could affect current responding. Contrary to what might be expected from recent theorizing, anticipation of future food delayed by an hour or more after the start of the work session had no effect on current performance. Food intake was high and constant during work sessions except for a prefeeding effect that occurred when the free session closely preceded the next day's work session. Also, an increase in the difficulty of the work schedule increased the amount of work and the maximum price paid for food as if the work session were the only time food was available. The results indicate the importance of considering temporal limits in theories that require animals to integrate input over time to determine the allocation of resources among alternatives.     

Comprehension of directly and indirectly stated main ideas and details in discourse by brain-damaged and non-brain-damaged listeners

Aphasic, right-hemisphere-damaged, and non-brain-damaged subjects heard short narrative paragraphs. Each paragraph contained four main ideas and one or more details related to each main idea. After each paragraph was presented, subjects' comprehension and retention of main ideas and details from the paragraph were tested. Some of the test items directly restated information from paragraphs and others paraphrased information from paragraphs. All groups of subjects remembered main ideas better than they remembered details, and no group of subjects was significantly affected by whether test items directly or indirectly stated information from paragraphs. Disfluent aphasic and right-hemisphere-damaged subjects' overall paragraphs comprehension scores were not significantly poorer than those of non-brain-damaged subjects. Fluent and mixed aphasic subjects' overall paragraph comprehension scores were significantly worse than those of non-brain-damaged and right-hemisphere-damaged subjects. Token Test and Boston Diagnostic Aphasia Examination auditory comprehension scores did not predict aphasic subjects' paragraph comprehension scores. right-hemisphere-damaged subjects' overall paragraph comprehension scores were not significantly those of non-brain-damaged and right-hemisphere-damaged subjects. Token Test and Boston Diagnostic Aphasia Examination auditory comprehension scores did not predict aphasic subjects' paragraph comprehension scores.     

Comprehension of main ideas and details in coherent and noncoherent discourse by aphasic and nonaphasic listeners

Aphasic and nonaphasic listeners' comprehension of main ideas and details within coherent and noncoherent narrative discourse was examined. Coherent paragraphs contained one topic to which all sentences in the paragraph related. Noncoherent paragraphs contained a change in topic with every third or fourth sentence. Each paragraph contained four main ideas and one or more details that related to each main idea. Listeners' responses to yes/no questions following each paragraph yielded the following results: (1) Nonaphasic listeners comprehended the paragraphs better than aphasic listeners. (2) Both aphasic and nonaphasic listeners comprehended main ideas better than they comprehended details. (3) Coherence did not affect comprehension of main ideas for either group. (4) Coherence did not affect comprehension of details by nonaphasic subjects. (5) Coherence affected comprehension of details by aphasic subjects, and their comprehension of details in coherent paragraphs was worse than their comprehension of details in noncoherent paragraphs. There was no significant correlation between Token Test scores and measures of paragraph comprehension.     

Sensitivity to lexical denotation and connotation in brain-damaged patients: A double dissociation?

Sets of words can be grouped in terms of their denotation (cold and warm both refer literally to temperature) or in terms of their connotation (cold and warm connote remoteness and intimacy, respectively). To assess whether these two facets of meaning are dissociable, unilaterally left- and right-hemisphere-damaged patients were presented with word triads and asked to group together the two words that were closest in meaning. Right-hemisphere-damaged patients showed a preserved sensitivity to denotation, and a selective insensitivity to connotative facets of meanings. In contrast, left-hemisphere-damaged patients exhibited a preserved sensitivity to connotation as well as a selective insensitivity to denotative aspects of meanings. Inasmuch as normal control subjects displayed a flexible sensitivity to both denotative and connotative aspects of meaning, the results suggest that unilateral brain damage selectively curtails use of one or the other major aspect of word meaning.     

The nature of the phonological disorder in conduction aphasia

Sequences of attempts to name pictured objects were used to examine phonological dysfunction in three diagnostic subgroups of aphasia. A prevalence of "phonologically-oriented sequences" (i.e., those sequences that contained only attempts with a phonological resemblance to the target word) was found to be a diagnostic criterion for conduction aphasia. When compared to a group of Broca's (n = 7) and Wernicke's (n = 5) aphasics, all the conduction aphasics (n = 6) produced proportionately more of such phonologically-oriented sequences on a picture naming test. An examination of the phonologically-oriented sequences produced by the conduction aphasics indicates that speech production in conduction aphasia involves dysfunction at an early stage of sound-encoding. The theoretical implications of this view are discussed.