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.     

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 measure of agreement for use with the Holland classification system

A measure of agreement for partially ordered data is suggested that makes use of the k categories with the highest ranks, the ranks of the remaining categories being disregarded. The proposed measure is applied to the Self-Directed Search in order to evaluate its agreement with occupational preference. Other forms of agreement in the Holland classification system can also be assessed by the proposed measure. Examples are congruence and husband-wife and counselor-client agreement.     

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.     

The effects of progressive relaxation on stress and diabetic control

Four insulin-requiring diabetic Ss were followed in single-S designs to measure the impact of progressive muscle relaxation training on blood glucose and stress levels. Measures of blood glucose, stress, activity and caloric intake were taken four times a day, along with a daily measure of anxiety. Two of the 4 Ss showed a significant decrease in blood glucose during treatment periods as compared to baseline measures. Similarly, 2 of the 4 Ss showed a significant decrease in stress levels during treatment. A multiple regression analysis revealed some significant relationships between blood glucose, stress, activity level and caloric intake. The results support previous studies that show relaxation techniques to be a viable aid in establishing greater diabetic control.     

Midi-level measurement of social anxiety in psychiatric and non-psychiatric samples

This paper reports the development and assessment of midi-level behavioral measures of social anxiety in the context of two experiments, one studying an analog student sample, the other a psychiatric sample. Judgments on nine categories of clinically practical midi-level behaviors (e.g. Facial Expression, Orienting, Sense of Timing), based on a review of the literature on human ethology and on pilot research, were compared to global judgments of social anxiety and social skill and to physiological arousal. Intraclass correlations exceeded 0.80 for judgments of the global and midi-level behavioral ratings on both samples. Results of correlational analyses indicated that while there were several significant predictors of global skill and anxiety among the midis, the magnitude of the relationship between midis and globals was stronger for the patient than the student sample. Further analyses based on S's heart rate (HR) reactivity suggested that while global ratings did not significantly predict H R in a high social anxiety situation, one midi-level behavioral rating (self-manipulations) did. The clinical utility of the newly developed measures is discussed with particular attention to their practicality for behavior therapy.     

Speech comprehension after unilateral injection of sodium amytal

A unilateral cerebral dominance model predicts that speech comprehension will be disrupted after injection of sodium amytal into one hemisphere but not after the other. This model was supported when an auditory receptive task involving relatively nonredundant stimuli similar to that contained in the Token Test (E. DeRenzi & L. Vignolo, 1962, Brain, 85, 665–687) was administered to 17 epileptic patients undergoing bilateral amytal injections.     

Measurement of adult performance on Piaget's water horizontality task

Three versions of Piaget's water-level-horizontality task (multiple choice, drawing, and apparatus tests) were administered to 121 female and 74 male adult volunteers. Sex differences and container orientation effects were replicated. Men were more accurate than women and horizontal and vertical container orientations evoked more accurate responses than oblique orientation. Reliability estimates ranged from .78 to .97 and correlations among the measures ranged from .78 to .88. The relative merits of alternative water-level testing and scoring methods and the orientation and type of stimuli to be used are discussed.