Canonical analysis of two convex polyhedral cones and applications

Canonical analysis of two convex polyhedral cones consists in looking for two vectors (one in each cone) whose square cosine is a maximum. This paper presents new results about the properties of the optimal solution to this problem, and also discusses in detail the convergence of an alternating least squares algorithm. The set of scalings of an ordinal variable is a convex polyhedral cone, which thus plays an important role in optimal scaling methods for the analysis of ordinal data. Monotone analysis of variance, and correspondence analysis subject to an ordinal constraint on one of the factors are both canonical analyses of a convex polyhedral cone and a subspace. Optimal multiple regression of a dependent ordinal variable on a set of independent ordinal variables is a canonical analysis of two convex polyhedral cones as long as the signs of the regression coefficients are given. We discuss these three situations and illustrate them by examples.     

Confidence in judgments based on incomplete information: An investigation using both hypothetical and real gambles

This study assessed how confidence in judgments is affected by the need to make inferences about missing information. Subjects indicated their likelihood of taking each of a series of gambles based on both probability and payoff information or only one of these sources of information. They also rated their confidence in each likelihood judgment. Subjects in the Explicit Inference condition were asked to explicitly estimate the values of missing information before making their responses while subjects in the Implicit Inference condition were not. The manner in which probability information was framed was also manipulated. Experiment 1 employed hypothetical gambles and Experiment 2 employed gambles with real money. Expressed likelihood of taking gambles was higher when probability was phrased in terms of '% chance of winning' rather than '% chance of losing', but this difference was somewhat less with real gambles than with hypothetical gambles. Confidence ratings in each experiment were actually higher on incomplete information trials than on complete information trials in the Explicit Inference condition. Results were related to the general issue of confidence in judgments.     

Effectiveness of the GOFER course in decision making for high school students

The paper describes and evaluates the GOFER course in decision making for high school students (Mann, Harmoni and Power, 1988). The course was based on principles from the conflict theory of decision making (Janis and Mann, 1977) and was designed to provide adolescents with an understanding of factors that produce good and poor decision making as well as knowledge and practice of sound decision skills. Two evaluation studies were conducted to examine effectiveness of the course. Study 1 was conducted with young adolescents (12 year olds). It found a significant difference between students trained in the course and a control group on measures of self-esteem as a decision maker, self reported decision habits and knowledge of decision strategy. Study 2 was conducted with mid-adolescents (15 year olds). It, too, found a significant difference between students who took the course and a control group on measures of self esteem as a decision maker and self-reported decision habits. It is concluded that while the evaluation study fell short of an ideal test, the GOFER course met the criteria of improving student knowledge, raising confidence in decision making and changing self reported decision habits.     

Examining differential item functioning due to item difficulty and alternative attractiveness

A method for analyzing test item responses is proposed to examine differential item functioning (DIF) in multiple-choice items through a combination of the usual notion of DIF, for correct/incorrect responses and information about DIF contained in each of the alternatives. The proposed method uses incomplete latent class models to examine whether DIF is caused by the attractiveness of the alternatives, difficulty of the item, or both. DIF with respect to either known or unknown subgroups can be tested by a likelihood ratio test that is asymptotically distributed as a chi-square random variable.     

An automated test development of parallel tests from a seed test

Binary programming models are presented to generate parallel tests from an itembank. The parallel tests are created to match item for item an existing seed test and match user supplied taxonomic specifications. The taxonomic specifications may be either obtained from the seed test or from some other user requirement. An algorithm is presented along with computational results to indicate the overall efficiency of the process. Empirical findings based on an itembank for the Arithmetic Reasoning section of the Armed Services Vocational Aptitude Battery are given.The Office of Naval Research, Program in Cognitive Science, N00014-87-C-0696 partially supported the work of Douglas H. Jones. The Rutgers Research Resource Committee of the Graduate School of Management partially supported the work of Douglas H. Jones and Ing-Long Wu. A Thomas and Betts research fellowship partially supported the work of Ing-Long Wu. The Human Resources Laboratory, United States Air Force, partially supported the work of Ronald Armstrong. The authors benefited from conversations with Dr. Wayne Shore, Operational Technologies, San Antonio, Texas. The order of authors' names is alphabetical and denotes equal authorship.     

Minimizing the number of observations: A generalization of the spearman-brown formula

A new method for determining the minimum number of observations per subject needed to achieve a specific generalizability coefficient is presented. This method, which consists of a branch-and-bound algorithm, allows for the employment of constraints specified by the investigator.     

Temporal proximity and reinforcement sensitivity in multiple schedules

Distributions of reinforcers between two components of multiple variable-interval schedules were varied over a number of conditions. Sensitivity to reinforcement, measured by the exponent of the power function relating ratios of responses in the two components to ratios of reinforcers obtained in the components, did not differ between conditions with 15-s or 60-s component durations. The failure to demonstrate the “short-component effect,” where sensitivity is high for short components, was consistent with reanalysis of previous data. With 60-s components, sensitivity to reinforcement decreased systematically with time since component alternation, and was higher in the first 15-s subinterval of the 60-s component than for the component whose total duration was 15 s. Varying component duration and sampling behavior at different times since component transition may not be equivalent ways of examining the effects of average temporal distance between components.     

Variable-interval schedules of timeout from avoidance

Rats were trained on concurrent schedules in which pressing one lever postponed shock and pressing the other occasionally produced a 2-min timeout during which the shock-postponement schedule was suspended and its correlated stimuli were removed. Throughout, the shock-postponement schedule maintained proficient levels of avoidance. Nevertheless, in Experiment 1 responding on the timeout lever was established rapidly, was maintained at stable levels on variable-interval schedules, was extinguished by withholding timeout, was reestablished when timeout was reintroduced, and was brought under discriminative control with a multiple variable-interval extinction schedule of timeout. These results are in contrast with Verhave's (1962) conclusion that timeout is an ineffective reinforcer when presented to rats on intermittent schedules. In Experiment 2 the consequence of responding on the timeout lever was altered so that the shock-postponement schedule remained in effect even though the stimulus conditions associated with timeout were produced for 2 min. Responding extinguished, indicating that suspension of the shock-postponement schedule, not stimulus change, was the source of reinforcement. By establishing the reinforcing efficacy of timeout with standard variable-interval schedules, these experiments illustrate a procedure for studying negative reinforcement in the same way as positive reinforcement.     

Auditory word discriminations in the pigeon.

Four pigeons were trained on a multiple variable-interval 30-s extinction schedule with various pairs of spoken English words presented as the discriminative stimuli. The birds typically produced discrimination indices of 70% to 90% accuracy. Discrimination accuracy was improved by shortening the interval between auditory stimulus presentations, and by increasing the number of syllables in the words.