Weighted minimum trace factor analysis

In the last decade several authors discussed the so-called minimum trace factor analysis (MTFA), which provides the greatest lower bound (g.l.b.) to reliability. However, the MTFA fails to be scale free. In this paper we propose to solve the scale problem by maximization of the g.l.b. as the function of weights. Closely related to the primal problem of the g.l.b. maximization is the dual problem. We investigate the primal and dual problems utilizing convex analysis techniques. The asymptotic distribution of the maximal g.l.b. is obtained provided the population covariance matrix satisfies sone uniqueness and regularity assumptions. Finally we outline computational algorithms and consider numerical examples.I wish to express my gratitude to Dr. A. Melkman for the idea of theorem 3.3.     

Preference for unsegmented interreinforcement intervals in concurrent chains

Five pigeons were trained under concurrent-chain schedules in which a pair of independent, concurrent variable-interval 60-s schedules were presented in the initial link and either both variable-interval or both fixed-interval schedules were presented in the terminal link. Except for the baseline, one of the terminal-link schedules was always a two-component chained schedule and the other was either a simple or a tandem schedule of equal mean interreinforcement interval. The values of the fixed-interval schedules were either 15 s or 60 s; that of the variable-interval schedules was always 60 s. A 1.5-s changeover delay operated during the initial link in some conditions. The pigeons preferred a simple or a tandem schedule to a chain. For the fixed-interval schedules, this preference was greater when the fixed interval was 60 s than when it was 15 s. For the variable-interval schedules, the preferences were less pronounced and occurred only when the changeover delay was in effect. For a given type of schedule and interreinforcement interval, similar preferences were obtained whether the nonchained schedule was a tandem or simple schedule. The changeover delay generally inflated preference and lowered the changeover rate, especially when the terminal-link schedules were either short (15 s) or aperiodic (variable-interval). The results were consistent with the notion that segmenting the interreinforcement interval of a schedule into a chain lowers the preference for it.     

Time-related processes in time-based prospective memory and in time-interval production

Time-based prospective memory tasks require the retrieval of previously formed plans (e.g., call me on my mobile phone) either at a specified time (e.g., at 3 p.m.) or after a specified period of time has elapsed (e.g., in 3 min). In the present study, we investigated whether the same time-related processes are recruited for a short-duration time-based prospective memory task and for a time-interval production task. In a dual-task paradigm, we required young adult participants to make category-membership decisions, while they were simultaneously engaged either in a time-based prospective memory tasks or in a time-interval production task. Under one set of conditions, participants were instructed to allocate attention equally to the two tasks, whereas in another set of conditions, they allocated attention primarily to the time-relevant task. The findings revealed that time estimates were not affected by the attention allocation manipulation, although it influenced performance on the concurrent category membership decision making task, and as expected time estimates were more accurate on the prospective memory task than on the time-production task. Based on the preponderance of the findings, we suggest that timing is managed by different mechanisms and/or strategies on time-interval production tasks and on short-duration time-based prospective memory tasks.     

Human performance on negative slope schedules of points exchangeable for money: a failure of molar maximization

Panel pressing was generated and maintained in 5 adult humans by schedules of points exchangeable for money. Following exposure to a variable-interval 30-s schedule and to a linear variable-interval 30-s schedule (which permitted points to accumulate in an unseen "store" in the absence of responding), subjects were exposed to a series of conditions with a point-subtraction contingency arranged conjointly with the linear variable-interval schedule. Specifically, points were added to the store according to the linear-variable interval 30-s schedule and were subtracted from the store according to a ratio schedule. Ratio value varied across conditions and was determined individually for each subject such that the subtraction contingency would result in an approximately 50% reduction in the rate of point delivery. Conditions that included the subtraction contingency were termed negative slope schedules because the feedback functions were negatively sloped across all response rates greater than the inverse of the variable-interval schedule, in this case, two per minute. Overall response rates varied inversely with the subtraction ratio, indicating sensitivity to the negative slope conditions, but were in excess of that required by accounts based on strict maximization of overall reinforcement rate. Performance was also not well described by a matching-based account. Detailed analyses of response patterning revealed a consistent two-state pattern in which bursts of high-rate responding alternated with periods of prolonged pausing, perhaps reflecting the joint influence of local and overall reinforcement rates.     

Effects of cocaine on performance under fixed-interval schedules with a small tandem ratio requirement

Daily administration of cocaine often results in the development of tolerance to its effects on responding maintained by fixed-ratio schedules. Such effects have been observed to be greater when the ratio value is small, whereas less or no tolerance has been observed at large ratio values. Similar schedule-parameter-dependent tolerance, however, has not been observed with fixed-interval schedules arranging comparable interreinforcement intervals. This experiment examined the possibility that differences in rate and temporal patterning between the two types of schedule are responsible for the differences in observed patterns of tolerance. Five pigeons were trained to key peck on a three-component multiple (tandem fixed-interval fixed-ratio) schedule. The interval values were 10, 30, and 120 s; the tandem ratio was held constant at five responses. Performance appeared more like that observed under fixed-ratio schedules than fixed-interval schedules. Effects of various doses of cocaine given weekly were then determined for each pigeon. A dose that reduced responding was administered prior to each session for 50 days. A reassessment of effects of the range of doses revealed tolerance. The degree of tolerance was similar across components of the multiple schedule. Next, the saline vehicle was administered prior to each session for 50 days to assess the persistence of tolerance. Tolerance diminished in all subjects. Overall, the results suggested that schedule-parameter-dependent tolerance does not depend on the temporal pattern of responding engendered by fixed-ratio schedules.     

Time and rate measures in choice transitions

Three experiments with pigeons studied the relation between time and rate measures of behavior under conditions of changing preference. Experiment 1 studied a concurrent chain schedule with random-interval initial links and fixed-interval terminal links; Experiment 2 studied a multiple chained random-interval fixed-interval schedule; and Experiment 3 studied simple concurrent random-interval random-interval schedules. In Experiment 1, and to a lesser extent in the other two experiments, session-average initial-link wait-time differences were linearly related to session-average response-rate differences. In Experiment 1, and to a lesser extent in Experiment 3, ratios of session-average initial-link wait times and response rates were related by a power function. The weaker relations between wait and response measures in Experiment 2 appear to be due to the absence of competition between responses. In Experiments 1 and 2, initial-link changes lagged behind terminal-link changes. These findings may have implications for the relations between fixed- and variable-interval procedures and suggest that more attention should be paid to temporal measures in studies of free-operant choice.     

Effects of reinforcer probability, delay, and response requirements on the choices of rats and pigeons: possible species differences

In Experiment 1 with rats, a left lever press led to a 5-s delay and then a possible reinforcer. A right lever press led to an adjusting delay and then a certain reinforcer. This delay was adjusted over trials to estimate an indifference point, or a delay at which the two alternatives were chosen about equally often. Indifference points increased as the probability of reinforcement for the left lever decreased. In some conditions with a 20% chance of food, a light above the left lever was lit during the 5-s delay on all trials, but in other conditions, the light was only lit on those trials that ended with food. Unlike previous results with pigeons, the presence or absence of the delay light on no-food trials had no effect on the rats' indifference points. In other conditions, the rats showed less preference for the 20% alternative when the time between trials was longer. In Experiment 2 with rats, fixed-interval schedules were used instead of simple delays, and the presence or absence of the fixed-interval requirement on no-food trials had no effect on the indifference points. In Experiment 3 with rats and Experiment 4 with pigeons, the animals chose between a fixed-ratio 8 schedule that led to food on 33% of the trials and an adjusting-ratio schedule with food on 100% of the trials. Surprisingly, the rats showed less preference for the 33% alternative in conditions in which the ratio requirement was omitted on no-food trials. For the pigeons, the presence or absence of the ratio requirement on no-food trials had little effect. The results suggest that there may be differences between rats and pigeons in how they respond in choice situations involving delayed and probabilistic reinforcers.     

Application of Sequential Interval Estimation to Adaptive Mastery Testing

In this paper, we apply sequential one-sided confidence interval estimation procedures with β-protection to adaptive mastery testing. The procedures of fixed-width and fixed proportional accuracy confidence interval estimation can be viewed as extensions of one-sided confidence interval procedures. It can be shown that the adaptive mastery testing procedure based on a one-sided confidence interval with β-protection is more efficient in terms of test length than a testing procedure based on a two-sided/fixed-width confidence interval. Some simulation studies applying the one-sided confidence interval procedure and its extensions mentioned above to adaptive mastery testing are conducted. For the purpose of comparison, we also have a numerical study of adaptive mastery testing based on Wald's sequential probability ratio test. The comparison of their performances is based on the correct classification probability, averages of test length, as well as the width of the “indifference regions.” From these empirical results, we found that applying the one-sided confidence interval procedure to adaptive mastery testing is very promising.     

Controlled and automatic uses of memory in depressed patients: effect of retention interval lengths

The present study examines controlled and automatic uses of memory in clinically depressed patients by applying the Process Dissociation Procedure developed by Jacoby (1991) to a stem completion memory task with short and long retention intervals. The results show that the contribution of controlled processes is lower in depressed patients than in controls, especially for the longest retention interval, whereas the contribution of automatic processes is equivalent in both groups and unaffected by the length of the retention interval. These findings are discussed in a cognitive control framework.     

Matching-to-sample accuracy on fixed-ratio schedules.

Pigeons performing on a matching-to-sample procedure were exposed to six fixed-ratio (FR) schedules (FR 1, 5, 10, 20, 40, and 60) of food reinforcement for correct matching responses. During both a correction and a noncorrection procedure without an intertrial interval (ITI), matching accuracy was lower on FR 1 and FR 60 than at intermediate ratios. With the FR 1 schedule, both a 5-sec and a 25-sec ITI resulted in higher matching accuracy than without an ITI; accuracy, with an ITI, was fairly constant for ratios of 1 to 20 but declined at higher ratios. The results suggest that the presence or absence of an ITI in matching to sample may account for inconsistencies obtained in earlier studies of the relationship of matching accuracy to ratio size.