Tests of symmetry in three-way contingency tables

Three-dimensional contingency tables are analyzed, with one variable (e.g., sex) as a factor, and with a natural relation between the other variables (e.g. left and right eye vision). Models of special interest, like symmetry and proportional symmetry between the related variables, and homogeneity across the factor levels, are investigated. Maximum likelihood estimators of parameters and partitions of chi-square goodness-of-fit statistics are explicitly presented; the independence of certain models is noted, and an example is discussed.     

Robust estimation of ability in the Rasch model

Estimating ability parameters in latent trait models in general, and in the Rasch model in particular is almost always hampered by noise in the data. This noise can be caused by guessing, inattention to easy questions, and other factors which are unrelated to ability. In this study several alternative formulations which attempt to deal with these problems without a reparameterization are tested through a Monte Carlo simulation. It was found that although no one of the tested schemes is uniformly superior to all others, a modified jackknife stood out as the best one in general, it was also super efficient (more efficient than the asymptotically optimal estimator) for tests with forty or fewer items. It is proposed that this sort of jackknifing scheme for estimating ability be considered for practical work.This research was funded through a grant from the Law Enforcement Assistance Administration (78-NI-AX-0047) to the Bureau of Social Science Research, Howard Wainer, Principal Investigator. We would like to thank Ronald Mead, Anne Morgan and James Ramsay for kind, generous, and invaluable help at various stages of the project.     

A stochastic model for test-retest correlations

A simple stochastic model is formulated in order to determine the optimal time between the first test and the second test when the test-retest method of assessing reliability is used. A forgetting process and a change in true score process are postulated. The optimal time between tests is derived by maximizing the probability that the respondent has not remembered the response on the first test and has not had a change in true score. The resulting test-retest correlation is then found to be a linear function of the true reliability of the test, where the slope of this function is the key probability of not remembering and having no change in true score. Some numerical examples and suggestions for using the results in empirical studies are given. Specific recommendations are presented for improved design and analysis of intentions data.This research was made possible by a grant from the Center for Food Policy Research, Graduate School of Business, Columbia University, New York, New York, 10027.     

Timing the second response in two-response avoidance.

Rats were trained on a free-operant avoidance task requiring two lever presses within R seconds, with the opportunity for each response distinguished by differing stimuli. Response latencies at a variety of response-shock intervals were found to be proportional to the time available for the response. These results are shown to be consonant with a scalar expectancy model of timing behavior.     

Parameter estimation in latent trait models

Latent trait models for binary responses to a set of test items are considered from the point of view of estimating latent trait parameters=( ₁, , _n ) and item parameters=( ₁, , _k ), where _j may be vector valued. With considered a random sample from a prior distribution with parameter, the estimation of (, ) is studied under the theory of the EM algorithm. An example and computational details are presented for the Rasch model.This work was supported by Contract No. N00014-81-K-0265, Modification No. P00002, from Personnel and Training Research Programs, Psychological Sciences Division, Office of Naval Research. The authors wish to thank an anonymous reviewer for several valuable suggestions.     

Choice, changeover, and travel: A quantitative model

Six pigeons were trained on concurrent variable-interval schedules in which responding on fixed-interval schedules was required to give access to the alternate schedule. Responding on the concurrent schedules was not allowed, after changing over had commenced, until the changeover schedule had been completed. In Parts 1 to 3 of the experiment, the changeover fixed-interval schedules were equal and were 0 s, 10 s, and 20 s, respectively. In each part, the relative frequency of reinforcement obtained on the concurrent schedules was varied over at least five conditions. In Part 4, the concurrent schedules were equal, and one changeover fixed-interval schedule was twice the other. Under these conditions, the absolute sizes of the changeover schedules were varied. Increasing the changeover requirement from 0 s to 10 s (Parts 1 and 2) resulted in increases in the sensitivity of behavior allocation to reinforcers obtained, but no further increase was obtained when the changeover schedules were increased to 20 s (Part 3). In Part 4, performance was biased towards the concurrent schedule that took less time to enter. These results are consistent with a subtractive punishment model of travel in which the degree of punishment is measured by the number of reinforcers apparently lost from a schedule when the subject changes to that schedule. Absolute times spent on the main keys could be accurately described by a previous model of changeover performance.     

Decomposing the encoding of action events: A dual conception

Two experiments are reported in which we tested the hypothesis that encoding of verbal features of subject-performed tasks or SPTs (e.g., bounce the ball, lift the spoon) is attention-demanding and effortful, whereas physical features of this memory task (e.g., color, weight) are acquired with little effort, and without deliberate encoding strategies. In Experiment 1, subjects were asked to perform a series of SPTs and were examined on recall of verbal instructions and colors of objects involved under conditions of focused or divided attention. In Experiment 2, performance of a series of SPTs was followed by recall of verbal instructions and recall of weights of objects involved. Results of both experiments indicated that recall of the verbal task component was negatively affected by requirements of dual-task performance, whereas recall of both physical task features was equally good in both encoding conditions. The obtained pattern of outcome is interpreted as supportive of the dual conception hypothesis of the nature of the encoding of action events.     

Analysis of the elements of attention: A neuropsychological approach

A model for conceptualizing the components or elements of attention is presented. The model substitutes for the diffuse and global concept of attention a group of four processes and links them to a putative system of cerebral structures. Data in support of the model are presented; they are derived from neuropsychological test scores obtained from two samples, the first consisting of 203 adult neuropsychiatric patients and normal control subjects, and the second, an epidemiologically-based sample of 435 elementary school children. Principal components analyses of test scores from these two populations yielded similar results: a set of independent elements of attention that are assayed by different tests. This work presents a heuristic for clinical research in which the measurement of attention is essential.     

Axiomatic and numerical conjoint measurement: An evaluation of diagnostic efficacy

Synthetic data are used to examine how well axiomatic and numerical conjoint measurement methods, individually and comparatively, recover simple polynomial generators in three dimensions. The study illustrates extensions of numerical conjoint measurement (NCM) to identify and model distributive and dual-distributive, in addition to the usual additive, data structures. It was found that while minimum STRESS was the criterion of fit, another statistic, predictive capability, provided a better diagnosis of the known generating model. That NCM methods were able to better identify generating models conflicts with Krantz and Tversky's assertion that, in general, the direct axiom tests provide a more powerful diagnostic test between alternative composition rules than does evaluation of numerical correspondence. For all methods, dual-distributive models are most difficult to recover, while consistent with past studies, the additive model is the most robust of the fitted models.Douglas Emery is now at the Krannert Graduate School of Management, Purdue University, West Lafayette, IN, on leave from the University of Calgary.     

RELATIVE EFFECTIVENESS OF TEACHER ATTENTION AND THE “GOOD BEHAVIOR GAME” IN MODIFYING DISRUPTIVE CLASSROOM BEHAVIOR1

A variety of behavioral procedures have been employed in recent years to modify disruptive classroom behavior. Such methods have been developed with the belief that curtailing disruptive behavior would strengthen positive classroom performance. In this study, two procedures, the good behavior game and the teacher-attention method, were compared to determine short-run effectiveness. Four teachers (two fourth-grade and two fifth-grade) implemented both methods in their classrooms over a five-week period. Presentation of methods was alternated in a counterbalanced design to control for order effects. Each of the four classrooms consisted of 25 students. A time-sampling procedure was used to record the presence or absence of disruptive behavior within 15-second intervals. Disruptive behavior was defined as any talking-out or out-of-seat behavior without permission. The results indicated that both procedures were effective in modifying disruptive classroom behavior, but that the good behavior game reduced disruptive behavior significantly better than the teacher-attention method. In addition, all teachers preferred the game to the teacher-attention procedure. This reaction seemed related to the effort involved in initiating the two activities. The good behavior game required less effort on the teacher's part. However, use of the game alone raises certain ethical considerations. One such issue involves abuse of peer pressure. Also, there is a possibility that negative rules may tend to promote resentment. Positively stated rules would ameliorate that problem. Another relates to the possibility that some teachers might be carried away by the ease of the game's implementation to the extent that behavior control becomes the primary objective in the classroom. As a result, one might consider use of the game to maximize short-term change, but then phase out this procedure in favor of another method (e.g., teacher attention) for long-run effects.