Estimation of stimulus-response curves by bayesian least squares

Bayesian least squares techniques are adapted to estimation of stimulus-response curves, rather broadly conceived. Illustrative examples deal with estimation of person characteristic curves and item characteristic curves in the context of mental testing, and estimation of a stimulus-response curve using data from a psychophysical experiment.The present paper is a version of an invited address of the same title, presented to the meetings of The Psychometric Society in Monterey, California on June 8, 1979, expanded by adding Example 1.The writer gratefully acknowledges the benefit of conversations with Don Pierce, and with John Shih, whose related work on density estimation pointed up an error in the original version of Section 2. He acknowledges, gratefully, support by the National Science Foundation through Grants MCS 76-02166A01 and MCS 78-01932. And he wishes to express his gratitude for the cordial hospitality and gracious cooperation offered by Professor Donald M. MacKay and the staff of the Department of Communication, University of Keele, during spring and summer, 1976; in particular, by Professor Dennis P. Andrews and Keichi Uchikawa, who kindly furnished data, a small portion of which is used in the illustrative example, Example 2.     

Response rate, latency, and resistance to change

Pigeons were trained on a multiple variable-interval/variable-interval schedule with pacing contingencies that generated high response rates in one component and low response rates in the other. Timeout periods separated the schedule components. During resistance-to-change tests, response-independent food was presented during the timeout periods, and the duration of that food presentation was varied among test sessions. Response rates in the schedule components decreased and latencies to the first response increased as a function of the duration of food presentations during the timeout. Both dependent measures changed about the same amount relative to their own baseline levels. The conclusions are that baseline response rates controlled by pacing contingencies are equally resistant to change, given equal reinforcement densities, and latency is a sensitive measure of resistance to change.     

A COMPREHENSIVE EVALUATION OF REINFORCER IDENTIFICATION PROCESSES FOR PERSONS WITH PROFOUND MULTIPLE HANDICAPS

We evaluated comprehensively a preference assessment for identifying reinforcers for persons with profound multiple handicaps. Four experiments were conducted involving 18 individuals. Results of Experiment 1 replicated previous findings in that the assessment identified student preferences for respective stimuli, and caregiver opinion of preferences did not coincide with the systematic assessment. Results of Experiment 2 indicated highly preferred stimuli were likely to function as reinforcers in training programs, whereas stimuli not highly preferred did not function as reinforcers. Results of Experiment 3 suggested the 12 stimuli used in the assessment represented a comprehensive stimulus set for identifying preferences, although the utility of the set sometimes could be enhanced by caregiver opinion. Results of Experiment 4 indicated the assessment identified preferences likely to be maintained over time. Overall, results are discussed in terms of identifying limits and alternatives to a behavioral teaching technology when applied to persons with profound multiple handicaps.     

Tolerance to and residual effects of cocaine in squirrel monkeys depend on reinforcement-schedule parameter.

Lever pressing by 4 squirrel monkeys was maintained under a three-component multiple fixed-ratio schedule of food presentation; components differed with respect to ratio size. For each monkey, acute administration of cocaine (0.03 to 1.3 mg/kg, i.m.) produced dose-dependent decreases in overall response rate in each component. During repeated daily administration of 1.0 mg/kg of cocaine, tolerance developed to the rate-decreasing effects under each of the ratio contingencies, but developed to a greater extent and was evident in earlier parts of sessions for performance under the smaller ratios. Response rates of 2 monkeys increased above nondrug control levels despite the putative reinforcer not being consumed during the session. When saline or a smaller dose of cocaine was substituted for 1.0 mg/kg, response rates often were suppressed below nondrug control-level responding. This suppressive effect was observed in each monkey and was more likely to be observed and/or to be of greater magnitude in large-ratio components for 3 of the 4 monkeys. When saline was administered chronically at the end of the chronic-drug phase, response rates remained suppressed in the large-ratio component for 2 of the monkeys. There was, therefore, a schedule-dependent dissociation between behavioral tolerance and the residual effects: Tolerance was greater when small ratios were arranged, whereas the residual effects were more pronounced when larger ratios were arranged.     

Maximum marginal likelihood estimation for semiparametric item analysis

The item characteristic curve (ICC), defining the relation between ability and the probability of choosing a particular option for a test item, can be estimated by using polynomial regression splines. These provide a more flexible family of functions than is given by the three-parameter logistic family. The estimation of spline ICCs is described by maximizing the marginal likelihood formed by integrating ability over a beta prior distribution. Some simulation results compare this approach with the joint estimation of ability and item parameters.IRCAMThe research reported in this paper was supported by Grants APA320 and A4035 from the Natural Sciences and Engineering Research Council of Canada. It was also supported by Contract No. F41689-82-C-10020 from the Air Force Human Resources Laboratory to Educational Testing Service. The author wishes to thank M. Abrahamowicz for his assistance and R. Darrell Bock for providing the parameters for the items used in the simulations.     

Fitting longitudinal reduced-rank regression models by alternating least squares

An alternating least squares method for iteratively fitting the longitudinal reduced-rank regression model is proposed. The method uses ordinary least squares and majorization substeps to estimate the unknown parameters in the system and measurement equations of the model. In an example with cross-sectional data, it is shown how the results conform closely to results from eigenanalysis. Optimal scaling of nominal and ordinal variables is added in a third substep, and illustrated with two examples involving cross-sectional and longitudinal data.Financial support by the Institute for Traffic Safety Research (SWOV) in Leidschendam, The Netherlands is gratefully acknowledged.     

Sensory superstition on multiple interval schedules.

Pigeons were exposed to multiple schedules in which an irregular repeating sequence of five stimulus components was correlated with the same reinforcement schedule throughout. Stable, idiosyncratic, response-rate differences developed across components. Components were rank-ordered by response rate; an approximately linear relation was found between rank order and the deviation of mean response rate from the overall mean rate. Nonzero slopes of this line were found for multiple fixed-interval and variable-time schedules and for multiple variable-interval schedules both when number of reinforcements was the same in all components and when it varied. The steepest function slopes were found in the variable schedules with relatively long interfood intervals and relatively short component durations. When just one stimulus was correlated with all components of a multiple variable-interval schedule, the slope of the line was close to zero. The results suggest that food-rate differences may be induced initially by different reactions to the stimuli and subsequently maintained by food.     

Choice and multiple reinforcers

Pigeons chose between equivalent two-component mixed and multiple terminal-link schedules of reinforcement in the concurrent-chains procedure. The pigeons preferred the multiple schedule over the mixed when the components of the compound schedules were differentiated in terms of density of reinforcement, but the pigeons were indifferent when the components were differentiated in terms of number of reinforcers per cycle. Taken together, these results indicate that a local variable, the interval to the first reinforcer, but not a molar variable, the number of reinforcers, was sufficient to differentiate the components and thereby evoke preference.     

Changes in a multiple-response repertoire during response-contingent punishment and response restriction: Sequential relationships

A multiple-response baseline of four activities was established using gerbils as subjects. When one of the baseline responses was punished (Experiment 1) or restricted (Experiments 2 and 3), only the most probable of the alternative baseline responses increased. The response most likely to follow the punished or restricted responses during baseline sessions was also suppressed during subsequent punishment or response-restriction treatment.     

An experimental analysis of the effects of d-amphetamine and cocaine on the acquisition and performance of response chains in monkeys.

In one component of a multiple schedule of food presentation, monkeys acquired a different four-response chain each session by responding sequentially on three keys in the presence of four geometric forms (learning). In the other component, the four-response chain was the same each session (performance). Both d-amphetamine and cocaine, at the higher doses, disrupted the behavior in the learning component; the overall response rate decreased, the overall accuracy was impaired (i.e., percent errors increased), and there was less within-session error reduction. The performance component was generally less sensitive than the learning component to the disruptive effects of both drugs on rate and accuracy. After pre-feeding or during an extended session, the response rate decreased in both components, but accuracy was generally unaffected. When the four discriminative stimuli in both components were removed, the behavior was disrupted to a greater extent in the performance component. The disruptive effects of both drugs on behavior in the learning component were attenuated when the drugs were administered during the session after the response chain had been acquired. It was concluded that the greater sensitivity of the learning component to disruptive drug effects is related to the relatively weak stimulus control and/or the lower rate of reinforcement associated with that component.