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.     

TEACHING THE HANDICAPPED TO EAT IN PUBLIC PLACES: ACQUISITION,GENERALIZATION AND MAINTENANCE OF RESTAURANT SKILLS

This study examined classroom-based instruction in restauranting skills for handicapped persons. Three male students were taught each of four skill components in sequential order: locating, ordering, paying, and eating and exiting. Training was implemented in a multiple baseline design across subjects and consisted of modeling and role playing in conjunction with photo slide sequences and a simulated ordering counter. The use of a menu containing general item classes and a finger matching procedure for identifying errors in the delivery of change greatly reduced the reading and math skills necessary to enter and complete the program. Periodic probes were conducted in a McDonald's restaurant prior to, during, and up to one-year following the termination of training. In addition, two probes (overt and covert observation) were conducted in a Burger King restaurant to assess further generalization to a location different from the one depicted throughout training. Results showed that students' performance on restaurant probes improved as a result of training, generalized to novel settings, maintained over an extended period of time, and was comparable to that of a normative sample of nonretarded persons.     

Effect of delay-interval stimuli on delayed symbolic matching to sample in the pigeon

In Experiment 1, food-deprived pigeons received delayed symbolic matching to sample training in a darkened Skinner box. Trials began with the illumination of the grain feeder lamp (no food sample), or illumination of this lamp, accompanied by the raising of the feeder tray (food sample). After a delay of a few seconds, the two side response keys were illuminated, one with red and one with green light, with positions counterbalanced over trials. Pecking the red (green) comparison produced grain reinforcement if the trial had started with food (no food); pecking red after a no-food sample or green after a food sample was not reinforced. Once matching performance was stable, four stimuli were presented during the delay interval, and their effects on matching accuracy were evaluated. Both illumination of the houselight and the center key with white geometric forms decreased matching accuracy, whereas presentation of a tone and vibration of the test chamber did not. In Experiment 2, pecking the red center key was reinforced with food according to a variable interval schedule. The effects of occasional brief presentations of the four stimuli used in the first experiment on ongoing pecking were assessed. The houselight and form disturbed key pecking, but the tone and vibration did not. Thus, stimuli that interfered with delayed matching also interfered with simple operant behavior. Implications of these results for theories of remembering are discussed.     

Self-control in pigeons under the Mischel paradigm

Walter Mischel studied self-control in preschool children in the following manner: if the child waited for an interval to end, he or she received the more preferred of two reinforcers; if the child responded to terminate the interval by ringing a bell, the less preferred reinforcer was given. We used an analogous procedure to study self-control in pigeons: if the bird waited for a trial to end, it received the more preferred reinforcer; if the bird terminated the trial by pecking a key, the less preferred reinforcer was given. We explored the effects on self-control of a number of variables analogous to those studied by Mischel and co-workers, e.g., presence versus absence of reinforcers, of alternative responses, and of stimuli during the wait interval; prior experience of the subjects; and test paradigm. The results obtained with pigeons paralleled the results obtained by Mischel with human children.     

Stimulus control of delayed matching in pigeons: Directed forgetting

Pigeons were trained in delayed matching-to-sample with two postsample stimuli. A postsample R-cue signaled that a matching choice phase would follow. A postsample F-cue signaled that a matching choice phase would not follow. Previous research found reduced matching accuracy on F-cued probe trials when comparison stimuli were presented in the choice phase. The present four experiments systematically varied the events following an F-cue to determine the conditions under which the F-cue reduces delayed-matching accuracy. When F-cues and R-cues controlled different behavior, matching on probe trials was poor. When both cues controlled the same behavior, matching on probe trials was good. This result is best explained by the theory that comparison stimuli retrieve the sample representation, but only in the behavioral context established by the R-cue. The present research supports the view that response-produced stimuli serve a contextual role in animal short-term memory.     

A bayesian approach to confirmatory factor analysis

Confirmatory factor analysis is considered from a Bayesian viewpoint, in which prior information on parameter is incorporated in the analysis. An iterative algorithm is developed to obtain the Bayes estimates. A numerical example based on longitudinal data is presented. A simulation study is designed to compare the Bayesian approach with the maximum likelihood method.Computer facilities were provided by the Computer Services Center, The Chinese University of Hong Kong.     

A stochastic multidimensional scaling procedure for the empirical determination of convex indifference curves for preference/choice analysis

The vast majority of existing multidimensional scaling (MDS) procedures devised for the analysis of paired comparison preference/choice judgments are typically based on either scalar product (i.e., vector) or unfolding (i.e., ideal-point) models. Such methods tend to ignore many of the essential components of microeconomic theory including convex indifference curves, constrained utility maximization, demand functions, et cetera. This paper presents a new stochastic MDS procedure called MICROSCALE that attempts to operationalize many of these traditional microeconomic concepts. First, we briefly review several existing MDS models that operate on paired comparisons data, noting the particular nature of the utility functions implied by each class of models. These utility assumptions are then directly contrasted to those of microeconomic theory. The new maximum likelihood based procedure, MICROSCALE, is presented, as well as the technical details of the estimation procedure. The results of a Monte Carlo analysis investigating the performance of the algorithm as a number of model, data, and error factors are experimentally manipulated are provided. Finally, an illustration in consumer psychology concerning a convenience sample of thirty consumers providing paired comparisons judgments for some fourteen brands of over-the-counter analgesics is discussed.     

Essential independence and likelihood-based ability estimation for polytomous items

A definition ofessential independence is proposed for sequences of polytomous items. For items satisfying the reasonable assumption that the expected amount of credit awarded increases with examinee ability, we develop a theory ofessential unidimensionality which closely parallels that of Stout. Essentially unidimensional item sequences can be shown to have a unique (up to change-of-scale) dominant underlying trait, which can be consistently estimated by a monotone transformation of the sum of the item scores. In more general polytomous-response latent trait models (with or without ordered responses), anM-estimator based upon maximum likelihood may be shown to be consistent for under essentially unidimensional violations of local independence and a variety of monotonicity/identifiability conditions. A rigorous proof of this fact is given, and the standard error of the estimator is explored. These results suggest that ability estimation methods that rely on the summation form of the log likelihood under local independence should generally be robust under essential independence, but standard errors may vary greatly from what is usually expected, depending on the degree of departure from local independence. An index of departure from local independence is also proposed.This work was supported in part by Office of Naval Research Grant N00014-87-K-0277 and National Science Foundation Grant NSF-DMS-88-02556. The author is grateful to William F. Stout for many helpful comments, and to an anonymous reviewer for raising the questions addressed in section 2. A preliminary version of section 6 appeared in the author's Ph.D. thesis.     

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.     

Community applications of instructional technology: teaching writers of instructional packages

A community education program, to develop a variety of performance competencies in large numbers of neighborhood residents, requires a technology for preparing learning units administerable by community members themselves. The effects of a writing manual, designed to teach nonprofessionals to prepare such instructional packages, were analyzed in two experiments. Experiment I employed a multiple-baseline design across three university student trainees. The results showed that appropriate program writing increased by 75% after completion of the manual. The results of Experiment II, with two low-income neighborhood residents serving as trainees, showed that packages produced by trained writers resulted in a greater increase in skill activities than sets of training stimuli produced by untrained writers.