The asymptotic posterior normality of the latent trait in an IRT model

It has long been part of the item response theory (IRT) folklore that under the usual empirical Bayes unidimensional IRT modeling approach, the posterior distribution of examinee ability given test response is approximately normal for a long test. Under very general and nonrestrictive nonparametric assumptions, we make this claim rigorous for a broad class of latent models.This research was partially supported by Office of Naval Research Cognitive and Neural Sciences Grant N0014-J-90-1940, 442-1548, National Science Foundation Mathematics Grant NSF-DMS-91-01436, and the National Center for Supercomputing Applications. We wish to thank Kumar Joag-dev and Zhiliang Ying for enlightening suggestions concerning the proof of the basic result.The authors wish to thank Kumar Joag-Dev, Brian Junker, Bert Green, Paul Holland, Robert Mislevy, and especially Zhiliang Ying for their useful comments and discussions.     

Some relationships between the information function of IRT and the signal/noise ratio and reliability coefficient of classical test theory

It is shown that IRTs information function for an item is functionally related to local versions of classical test theories' signal/noise ratio and reliability coefficient.     

A generalized family of coefficients of relational agreement for numerical scales

A family of coefficients of relational agreement for numerical scales is proposed. The theory is a generalization to multiple judges of the Zegers and ten Berge theory of association coefficients for two variables and is based on the premise that the choice of a coefficient depends on the scale type of the variables, defined by the class of admissible transformations. Coefficients of relational agreement that denote agreement with respect to empirically meaningful relationships are derived for absolute, ratio, interval, and additive scales. The proposed theory is compared to intraclass correlation, and it is shown that the coefficient of additivity is identical to one measure of intraclass correlation.The author thanks the Editor and anonymous reviewers for helpful suggestions.     

ASSESSING FOOD PREFERENCES AMONG PERSONS WITH PROFOUND MENTAL RETARDATION: PROVIDING OPPORTUNITIES TO MAKE CHOICES

Increased attention has been directed recently to assisting persons with severe handicaps to express preferences concerning events in their lives. We evaluated a program for assessing choice-making skills to provide opportunities for persons with profound mental retardation to express food and drink preferences. In Experiment 1, the assessment procedure involving repeated, paired-item presentations resulted in active choice making and the identification of preferences for all 5 participants. Results also indicated that caregiver opinion was not predictive of participant food and drink preferences. A survey of service providers supported the importance of meal-related choices in this population. In Experiment 2, the practicality of the assessment procedure was supported by demonstrating that (a) routine caregivers could apply the procedure with appropriate supervision to provide choice opportunities, and (b) results of the procedure were predictive of participant choices when a less structured and more normal opportunity to express a preference was provided during regular mealtimes. Results are discussed in terms of extending the developing technology of preference and reinforcer identification to other important areas for persons with severe disabilities.     

EFFECTS OF CHOSEN VERSUS ASSIGNED JOBS ON THE WORK PERFORMANCE OF PERSONS WITH SEVERE HANDICAPS

We evaluated the effects of several choice-related variables on the work performance of adults with severe handicaps. After assessing client work preferences, three choice-related situations were presented: (a) providing clients with the opportunity to choose a work task, (b) assigning a preferred task, and (c) assigning a nonpreferred task. Results indicated that clients attended to work tasks almost twice as much when they chose their tasks and when assigned to work on preferred tasks versus when assigned to work on nonpreferred tasks. Results are discussed regarding the need to assess systematically the effects of choice-related variables.     

Unification of models for choice between delayed reinforcers.

Two models for choice between delayed reinforcers, Fantino's delay-reduction theory and Killeen's incentive theory, are reviewed. Incentive theory is amended to incorporate the effects of arousal on alternate types of behavior that might block the reinforcement of the target behavior. This amended version is shown to differ from the delay-reduction theory in a term that is an exponential in incentive theory and a difference in delay-reduction theory. A power series approximation to the exponential generates a model that is formally identical with delay-reduction theory. Correlations between delay-reduction theory and the amended incentive theory show excellent congruence over a range of experimental conditions. Although the assumptions that gave rise to delay-reduction theory and incentive theory remain different and testable, the models deriving from the theories are unlikely to be discriminable by parametric experimental tests. This congruence of the models is recognized by naming the common model the delayed reinforcement model, which is then compared with other models of choice such as Killeen and Fetterman's (1988) behavioral theory of timing, Mazur's (1984) equivalence rule, and Vaughan's (1985) melioration theory.     

Modeling item responses when different subjects employ different solution strategies

A model is presented for item responses when different subjects employ different strategies, but only responses, not choice of strategy, can be observed. Using substantive theory to differentiate the likelihoods of response vectors under a fixed set of strategies, we model response probabilities in terms of item parameters for each strategy, proportions of subjects employing each strategy, and distributions of subject proficiency within strategies. The probabilities that an individual subject employed the various strategies can then be obtained, along with a conditional estimate of proficiency under each. A conceptual example discusses response strategies for spatial rotation tasks, and a numerican example resolves a population of subjects into subpopulations of valid responders and random guessers.The first author's work was supported by Contract No. N00014-85-K-0683, project designation NR 150-539, from the Cognitive Science Program, Cognitive and Neural Sciences Division, Office of Naval Research. We are grateful to Murray Aitkin, Isaac Bejar, Neil Dorans, Frederiksen, and Marklyn Wingersky for their comments and suggestions, and to Alison Gooding, Maxine Kingston, Donna Lembeck, Joling Liang, and Kentaro Yamamoto for their assistance with Example 2.