Matching, maximizing, and hill-climbing

In simple situations, animals consistently choose the better of two alternatives. On concurrent variable-interval variable-interval and variable-interval variable-ratio schedules, they approximately match aggregate choice and reinforcement ratios. The matching law attempts to explain the latter result but does not address the former. Hill-climbing rules such as momentary maximizing can account for both. We show that momentary maximizing constrains molar choice to approximate matching; that molar choice covaries with pigeons' momentary-maximizing estimate; and that the “generalized matching law” follows from almost any hill-climbing rule.     

Aftereffects of reinforcement on variable-ratio schedules

On each of variable-ratio 10, 40, and 80 schedules of reinforcement, when rats' lever-pressing rates were stable, the concentration of a liquid reinforcer was varied within sessions. The duration of the postreinforcement pause was an increasing function of the reinforcer concentration, this effect being more marked the higher the schedule parameter. The running rate, calculated by excluding the postreinforcement pause, was unaffected by concentration. The duration of the postreinforcement pause increased with the schedule parameter, but the proportion of the interreinforcement interval taken up by the pause decreased. Consequently, the overall response rate was an increasing function of the schedule parameter; i.e., it was inversely related to reinforcement frequency, contrary to the law of effect. The running rate, however, decreased with the reinforcement frequency, in accord with the law of effect. When 50% of reinforcements were randomly omitted, the postomission pause was shorter than the postreinforcement pause, but the running rate of responses was not affected.     

Effects of magnitude of food reinforcement on free-operant response rates

In Experiment 1 rats were trained to press a lever on a variable-ratio schedule of food presentation and were then exposed to progressively increasing magnitudes of food reinforcement. Response running rates (rates exclusive of the postreinforcement pause) were found to increase as a function of increasing reinforcement magnitudes. The effect of reinforcement magnitude on response rates inclusive of the postreinforcement pause, however, was less pronounced. Increases in the magnitude of reinforcement were also found to increase the length of the postreinforcement pause. Rats in Experiment 2 were trained to respond on a chained differential-reinforcement-of-low-rate variable-ratio schedule, and were exposed to increasing magnitudes of reinforcement as in Experiment 1. Response running rates increased in the variable-ratio component but decreased in the other component of the schedule. The results are discussed with reference to incentive accounts of reinforcement and the action of reinforcement on the response units generated by the operative contingencies.     

Items bundles

An item bundle is a small group of multiple choice items that share a common reading passage or graph, or a small group of matching items that share distractors. Item bundles are easily identified by paging through a copy of a test. Bundled items may violate the latent conditional independence assumption of unidimensional item response theory (IRT), but such a violation would not typically suggest the existence of a new fundamental human ability to read one specific reading passage or to interpret one specific graph. It is important, therefore, to have theoretical concepts and empirical checks that distinguish between, on the one hand, anticipated violations of latent conditional independence within item bundles, and, on the other hand, violations that cannot be attributed to idiosyncratic features of test format and instead suggest departures from unidimensionalty. To this end, two theorems on unidimensional IRT are extended to describe observable item response distributions when there is conditional independencebetween but not necessarilywithin item bundles.The author is grateful to Ivo Molenaar and the referees for many helpful suggestions, and to D. Thayer for assistance with computing.     

Maximum likelihood estimation of polyserial correlations

This paper considers a multivariate normal model with one of the component variables observable only in polytomous form. The maximum likelihood approach is used for estimation of the parameters in the model. The Newton-Raphson algorithm is implemented to obtain the solution of the problem. Examples based on real and simulated data are reported.The research of the first author was supported in part by a research grant (DA01070) from the US Public Health Service. We are indebted to the referees and the editor for some very valuable comments and suggestions.     

Pentobarbital and d-amphetamine effects on concurrent performances.

The effects of pentobarbital and d-amphetamine were studied in pigeons responding under several concurrent fixed-ratio variable-interval and concurrent fixed-ratio fixed-interval schedules of food presentation. Drug effects were compared with different fixed ratios, fixed and variable intervals, changeover delays, and with the schedules operating singly. Doses of d-amphetamine that increased or did not affect responding under the interval schedules decreased responding under the fixed-ratio schedule, whereas doses of pentobarbital that increased responding under the fixed-ratio schedule decreased or eliminated responding under the interval schedules. These effects depended both on the schedule of food delivery and the parameters of schedules arranged concurrently. Pentobarbital increased responding under the fixed-ratio schedule with 4-minute and 10-minute interval schedules arranged concurrently, but not with 1.5-minute schedules. d-Amphetamine decreased concurrent ratio and interval responding with the 1.5-minute interval schedules, but either increased or did not affect responding with the longer intervals. Changes in the parameter of one schedule altered responding controlled by that schedule and also other concurrent performances. As a consequence, the effects of drugs on each behavior were altered.     

Effect of variable-interval punishment on the behavior of humans in variable-interval schedules of monetary reinforcement

One male and three female human subjects pressed a button for monetary reinforcement under a range of variable-interval schedules specifying different frequencies of reinforcement. On alternate days, responding was also punished (by subtraction of money) according to a variable-interval 170-second schedule. In the absence of punishment, the rate of responding was an increasing negatively accelerated function of reinforcement frequency, as predicted by Herrnstein's equation. The effect of the punishment schedule was to suppress responding under lower frequencies of reinforcement; responding under higher reinforcement frequencies was much less affected. This was reflected in an increase in the value of K_H (the constant expressing the reinforcement frequency corresponding to the half-maximal response rate), whereas there was no significant change in the value of R_max (the constant expressing the maximum response rate). Previous results had shown that variable-ratio punishment resulted in a change in the values of both constants (Bradshaw, Szabadi, and Bevan, 1977). The results of the present study were consistent with the concept that the suppressive effects of punishment on responding depend on the nature of the punishment schedule.     

A TEST OF THE FORMAL AND MODERN THEORIES OF MATCHING

Pigeons' choosing between fixed-interval and random-interval schedules of reinforcement was investigated in three experiments using a discrete-trial procedure. In all three experiments, the random-interval schedule was generated by sampling a probability distribution at an interval (and in multiples of the interval) equal to that of the fixed-interval schedule. Thus the programmed delays to reinforcement on the random alternative were never shorter and were often longer than the fixed interval. Despite this feature, the fixed schedule was not strongly preferred. Increases in the probability used to generate the random interval resulted in decreased preferences for the fixed schedule. In addition, the number of consecutive choices on the preferred alternative varied directly with preference, whereas the consecutive number of choices on the nonpreferred alternative was fairly constant. The probability of choosing the random alternative was unaffected by the immediately prior interval encountered on that schedule, even when it was very long relative to the average value. The results loosely support conceptions of a "preference for variability" from foraging theory and the "utility of behavioral variability" from human decision-making literatures.     

The sensitivity of response rate to the rate of variable-interval reinforcement for pigeons and rats: a review

The relation between the rate of a response (B) and the rate of its reinforcement (R) is well known to be approximately hyperbolic: B = kR/(R + Ro), where k represents the maximum response rate, and Ro indicates the rate of reinforcers that will engender a response rate equal to half its maximum value. A review of data reported in 17 published papers revealed that, under variable-interval schedules of reinforcement, Ro was usually lower when pigeons were the subjects than when rats were the subjects. The value of k, in contrast, did not differ consistently between pigeons and rats. Some accounts interpret Ro as the rate of alternative, unscheduled reinforcers in the situation, expressed in units of the scheduled reinforcer. So interpreted, the difference in Ro implies that less alternative reinforcement (relative to the scheduled reinforcement) typically is available to pigeons in their operant conditioning chambers than it is to rats in theirs. Whether or not that interpretation of Ro is valid, the pigeon-rat difference in Ro ensures that for reinforcer rates above about 10 per hour, response rate will be noticeably less sensitive to changes in reinforcer rate (and presumably to changes in other incentive and motivational operations) with pigeons than with rats as subjects, at least with the experimental conditions typically employed.