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.     

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 eyewitness paradox

Two methods of analysing data from an identification parade give rise to seemingly contradictory outcomes, both of which reach statistical significance. The traditional method is based on the first choices of eyewitnesses, whereas the paired-comparison method takes account of each eyewitness's full rank ordering of the lineup participants. The person that most eyewitnesses pick out as the perpetrator of an offence (according to the first-choice method) may in fact be the person that those same eyewitnesses as a group regard as least likely to have committed the act (according to the paired-comparison method). Implications of the paradox for the analysis of lineup data are considered.     

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.     

Determination of a behavioral transfer function: White-noise analysis of session-to-session response-ratio dynamics on concurrent VI VI schedules

Six pigeons were exposed to concurrent variable-interval schedules in which the programmed reinforcer ratios changed from session to session according to a pseudorandom binary sequence. This procedure corresponded to the stochastic identification paradigm (“white-noise experiment”) of systems theory and enabled the relation between log response ratios in the current session and log reinforcer ratios in all previous sessions to be determined. Such dynamic relations are called linear transfer functions. Both nonparametric and parametric representations of these, in the form of “impulse-response functions,” were determined for each bird. The session-to-session response ratios resulting from the session-to-session pseudorandom binary variations in reinforcer ratios were well predicted by the impulse-response functions identified for each pigeon. The impulse-response functions were well fitted by a second-order dynamic model involving only two parameters: a time constant and a gain. The mean time constant was 0.67 sessions, implying that the effects of abrupt changes in log reinforcer ratios should be 96% complete within about five sessions. The mean gain was 0.53, which was surprisingly low inasmuch as it should equal the sensitivity to reinforcement ratio observed under steady-state conditions. The same six pigeons were subjected to a similar experiment 10 months following the first. Despite individual differences in impulse-response functions between birds within each experiment, the impulse-response functions determined from the two experiments were essentially the same.     

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.     

Forced classification: A simple application of a quantification method

This study formulates a property of a quantification method, the principle of equivalent partitioning (PEP). When the PEP is used together with Guttman's principle of internal consistency (PIC) in a simple way, the combination offers an interesting way of analyzing categorical data in terms of the variate(s) chosen by the investigator, a type of canonical analysis. The study discusses applications of the technique to multiple-choice, rank-order, and paired comparison data.This study was supported by the Natural Sciences and Engineering Research Council of Canada (Grant No. A7942). Comments on the earlier drafts from anonymous reviewers and the editor were much appreciated.     

Reinforcer pathology,probabilistic choice,and medication adherence in patients with multiple sclerosis

The reinforcer pathology model posits that core behavioral economic mechanisms, including delay discounting and behavioral economic demand, underlie adverse health decisions and related clinical disorders. Extensions beyond substance use disorder and obesity, however, are limited. Using a reinforcer pathology framework, this study evaluates medical adherence decisions in patients with multiple sclerosis. Participants completed behavioral economic measures, including delay discounting, probability discounting, and a medication purchase task. A medical decision-making task was also used to evaluate how sensitivity to mild side effect risk and efficacy contributed to the likelihood of taking a hypothetical disease-modifying therapy. Less steep delay discounting and more intense (greater) medication demand were independently associated with greater adherence to the medication decision-making procedure. More generally, the pattern of interrelations between the medication-specific and general behavioral economic metrics was consistent with and contributes to the reinforcer pathology model. Additional research is warranted to expand these models to different populations and health behaviors, including those of a positive health orientation (i.e., medication adherence).