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.     

Superimposition of response-independent reinforcement

Studies that have superimposed response-independent reinforcement (or reinforcers scheduled by contingencies placed on the absence of responding) upon conventional response-dependent schedules are reviewed. In general, providing alternative sources of reinforcement reduced response rates below the levels observed when alternative reinforcement was absent. However, response-rate elevation was sometimes found, particularly when rates of superimposed response-independent reinforcement were low. Superimposition of schedules providing reinforcers contingent on the absence of responding usually produced more severe response-rate decrements than superimposition of response-independent reinforcement. A variant of Herrnstein's equation, which assumes that some of the alternative reinforcers function as if they were delivered by baseline response-dependent source of reinforcement, is in qualitative agreement with the overall body of results obtained, and can predict both increases and decreases in response rate as resulting from superimposed reinforcers.     

Varying response-reinforcer contiguity in a recycling conjunctive schedule

Three experiments describe the effects of manipulating the frequency of response-reinforcer contiguity in a recycling conjunctive schedule. The schedule arranged that a reinforcer was delivered after 30 s provided at least one response had occurred; otherwise the next cycle started immediately. In Experiment 1, this schedule produced the typical pause–respond–pause pattern, with most responses at mid-interval; and, when a limited number of contiguities between responses and food delivery were added, the pattern became more like the monotonic scallop seen on fixed-interval schedules. In Experiment 2, the schedule was initially presented with an additional contingency that allowed contiguity on every trial. Fixed-interval-like behavior occurred and tended to persist as contiguities were gradually eliminated. In Experiment 3, the recycling conjunctive schedule alternated with a condition in which a large number of contiguities occurred. The pause–respond–pause pattern and fixed-interval-like performance occurred with few or many contiguities, respectively. The results of all three experiments illustrate how contiguity interacts with a small number of other variables to determine performance on interval schedules and illuminate previous findings with fixed-interval and fixed-time schedules.     

Money versus pain: experimental study of a conflict in humans.

Ten healthy human males volunteered to be subjects in an experiment in which they were to be paid to endure a painful sensation. This sensation was produced by isometric muscular contraction in the thighs. For each of six sessions the subjects received either a payment that was changed for each session (0.2, 0.5, 1.25, 3.125, 7.8125 French francs per 20 s) or a lump sum. At the beginning of a session, the subjects assumed a seated position against a wall, but without a seat, and the duration for which they could hold this position was the chief variable measured. Heart rate, blood pressure, and magnitude estimation of pain were also recorded periodically throughout each session. Pain was reported after a mean delay of 15 +/- 7 s (SE), and the magnitude estimates then increased linearly with time. The duration of maintaining the painful position increased linearly in relation to the logarithm of the increase in the amount of payment. Thus, utility of money decreased when pitted against pain.     

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.     

Units of analysis and kinetic structure of behavioral repertoires

It is suggested that molar streams of behavior are constructed of various arrangements of three elementary constituents (elicited, evoked, and emitted response classes). An eight-cell taxonomy is elaborated as a framework for analyzing and synthesizing complex behavioral repertoires based on these functional units. It is proposed that the local force binding functional units into a smoothly articulated kinetic sequence arises from temporally arranged relative response probability relationships. Behavioral integration is thought to reflect the joint influence of the organism's hierarchy of relative response probabilities, fluctuating biological states, and the arrangement of environmental and behavioral events in time.     

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.     

Self-selection biases in correlational studies based on questionnaires

It is commonly held that even where questionnaire response is poor, correlational studies are affected only by loss of degrees of freedom or precision. We show that this supposition is not true. If the decision to respond is correlated with a substantive variable of interest, then regression or analysis of variance methods based upon the questionnaire results may be adversely affected by self-selection bias. Moreover such bias may arise even where response is 100%. The problem in both cases arises where selection information is passed to the score indirectly via the disturbance or individual effects, rather than entirely via the observable explanatory variables. We suggest tests for the ensuing self-selection bias and possible ways of handling the ensuing problems of inference.The author would like to thank members of the Psychology Department at UWA for references on the illustrative example, namely the effects of sex-stereotyping on achievements in mathematics; thanks are also due to the anonymous reviewers whose comments resulted in material improvements to the paper.     

Psychopathology subtypes and symptom correlates among former prisoners of war

Psychopathology and symptom patterns were studied in 60 former prisoners-of-war (POWs) by administering standardized tests including the Minnesota Multiphasic Personality Inventory (MMPI), an adjustment problem checklist, and a structured clinical interview. Most POWs showed marked psychological impairment, but modal profile analysis identified two prototypic MMPI patterns, which differed in pervasiveness and type of psychopathology. Profile subtypes were defined by unique clusters of clinical symptoms and differed in confinement stress severity. The typology of symptoms argues against a homogeneous conceptualization of stress-induced disorders and suggests the need for definition of the severity and subtype of stress phenomena and individual difference factors in responding to trauma.