On approximate confidence intervals for measures of concordance

The use ofU-statistics based on rank correlation coefficients in estimating the strength of concordance among a group of rankers is examined for cases where the null hypothesis of random rankings is not tenable. The studentizedU-statistics is asymptotically distribution-free, and the Student-t approximation is used for small and moderate sized samples. An approximate confidence interval is constructed for the strength of concordance. Monte Carlo results indicate that the Student-t approximation can be improved by estimating the degrees of freedom.Research partially supported on ONR Contract N00014-82-K-0207.     

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.     

Uninstructed human responding: Sensitivity of low-rate performance to schedule contingencies

College students' presses on a telegraph key occasionally turned on a light in the presence of which button presses produced points later exchangeable for money. Initially, responding was maintained by low-rate contingencies superimposed on either random-interval or random-ratio schedules. Later, the low-rate contingencies were relaxed. Low-rate key pressing had been established for some students by shaping and for others by demonstration and written instructions. After the low-rate contingencies were relaxed, higher response rates generally did not increase point earnings with random-interval scheduling, but did so with random-ratio scheduling. In both cases, shaped responding usually increased, and instructed responding usually continued at an unchanged low rate. The insensitivity of instructed responding typically occurred despite contact with the contingencies. The differential sensitivity to schedule contingencies of shaped responding relative to instructed responding is consistent with the different properties of contingency-governed and rule-governed behavior and is not rate-dependent.     

Time, trace, memory

Objections to a trace hypothesis for interval timing do not apply to the multiple-time-scale (MTS) theory, which incorporates a dynamic trace tuned by the system history and can easily accommodate interval timing over a 1,000:1 range. The MTS model can also account for Weber's law as well as systematic deviations from it. Contrary to our critics, we contend that patterns of variance in interval timing experiments are not fully described by scalar expectancy theory, and that attempting to understand timing by assigning variance to different elements of a flexible model that lacks inductive support is a flawed strategy, because the attempt may be successful even if the model is wrong. We further argue that biological plausibility is an unreliable guide to the development of behavioral theory, that prediction is not the same as test, that induction should precede deduction, and that a rat is not a clock.     

Titration of schedule parameters by pigeons

Pigeons were tested in a computer-controlled two-key chamber. A standard (nonchanging) schedule of reinforcement was in force on one key, and an adjusting schedule on the other. The schedules were available concurrently after each reinforcement, but after the first peck on either key (the choice peck), the schedule on the other key was made inoperative. The parameter of the adjusting schedule was decreased when the standard schedule was chosen and increased when the adjusting schedule was chosen. The standard schedule was changed only between sessions. Fixed intervals and fixed ratios were used as standard schedules, and intervals and ratios were used as adjusting schedules. When standard and adjusting schedules were of the same type, median parameters on the adjusting key equalled those of the standard schedules, at four values of each standard schedule. For four of five birds, and for the group median, similar curves could be plotted through the indifference points obtained from a standard ratio with an adjusting interval, and from a standard interval with an adjusting ratio. These points showed consistent individual differences, but they could be predicted by assuming that the median time from the choice peck to reinforcement should be the same on both keys. This is equivalent to treating the schedule as a concurrent chain and assuming that Herrnstein's quantitative law of effect applies.     

Species differences in temporal control of behavior

Temporal control of rats' and pigeons' responding was analyzed and compared in detail on fixed-interval and fixed-time schedules with parameters of 30, 60, and 120 seconds. On fixed-time schedules, rats' responding decreased greatly or ceased, whereas pigeons continued to respond, especially on low schedule values. The running rate of responses (calculated by excluding the postreinforcement pause) was related to the duration of the preceding postreinforcement pause for rats but not for pigeons. Changes in response rate in successive segments of the interval were best described by normal curves. The relationship between midpoints of the normal curves and schedule value was a power function, with an exponent of less than one for pigeons but greater than one for rats. These differences could be explained in terms of a basic difference between the key-peck and lever-press responses, the two being differently affected by the response-eliciting properties of food.     

Preference for simple interval schedules of reinforcement in concurrent chains: Effects of segmentation ratio

A concurrent-chains procedure was used to examine pigeons' preferences between segmented and unsegmented terminal-link schedules of reinforcement. During the initial link, a pair of independent, concurrent variable-interval 60-s schedules was in effect. In the terminal link, reinforcement was provided by a chain fixed-interval fixed-interval schedule on one key and by a simple fixed-interval schedule with an equal interreinforcement interval in the other. The relative duration between the first and second components (segmentation ratio) in the terminal-link chained schedule was systematically varied while the terminal-link duration was kept constant at either 15 s or 30 s in two sets of conditions. With few exceptions, the simple schedule was preferred to the chained schedule. Furthermore, this preference was inversely related to the size of the segmentation ratio in the segmented schedule. When the segmentation ratio was smaller than 1:1, preference was more extreme for a 30-s condition than for a 15-s condition. However, preference decreased more rapidly in conditions with the longer terminal-link duration when the ratio increased. Taken together, these results were consistent with previous findings concerning the effect of the terminal-link duration on choice between segmented and unsegmented schedules. In addition, the data suggested that segmentation ratio in a segmented schedule constitutes another potent factor influencing preference for the unsegmented schedule.     

Methods of time sampling: A reappraisal of momentary time sampling and partial interval recording

We compared the accuracy of momentary time sampling (MTS) and partial interval recording (PIR) in estimating both absolute behavioral levels and relative change. A computer randomly generated runs of pseudobehavior varying in duration and rate and simulated MTS and PIR of each run. Results indicated that when estimating absolute behavioral levels, duration rather than rate should be used as the dependent measure, and MTS is more accurate than PIR. In contrast, PIR is the more sensitive method for detecting relative changes in behavioral levels, although, at high rates, PIR tends to underestimate the degree of change.     

Choice with a fixed requirement for food, and the generality of the matching relation

Pigeons were trained on choice procedures in which responses on each of two keys were reinforced probabilistically, but only after a schedule requirement had been met. Under one arrangement, a fixed-interval choice procedure was used in which responses were not reinforced until the interval was over; then a response on one key would be reinforced, with the effective key changing irregularly from interval to interval. Under a second, fixed-ratio choice procedure, responses on either key counted towards completion of the ratio and then, once the ratio had been completed, a response on the probabilistically selected key would produce food. In one experiment, the schedule requirements were varied for both fixed-interval and fixed-ratio schedules. In the second experiment, relative reinforcement rate was varied. And in a third experiment, the duration of an intertrial interval separating choices was varied. The results for 11 pigeons across all three experiments indicate that there were often large deviations between relative response rates and relative reinforcement rates. Overall performance measures were characterized by a great deal of variability across conditions. More detailed measures of choice across the schedule requirement were also quite variable across conditions. In spite of this variability, performance was consistent across conditions in its efficiency of producing food. The absence of matching of behavior allocation to reinforcement rate indicates an important difference between the present procedures and other choice procedures; that difference raises questions about the specific conditions that lead to matching as an outcome.     

Rapid determinations of preference in multiple concurrent-chain schedules.

With concurrent chains arranged for a pigeon's key pecks, pecks on two concurrently available initial-link keys (left and right) respectively produce separately operating terminal links (A and B). Preferences for terminal link A over terminal link B are usually calculated as deviations of relative initial-link response rates (left divided by total pecks) from those during baseline conditions, when A equals B. Baseline preferences, however, are often variable and typically are determined indirectly (e.g., with unequal A and B, reversing left-right assignments of A and B over sessions and estimating the baseline from differences between the relative rates generated). Multiple concurrent-chain schedules, with components each consisting of a pair of concurrent chains, speed the determination of preferences by arranging A and B and their reversal within sessions. In two experiments illustrating the feasibility of this procedure, one component operated with circles projected on initial-link keys and the other with pluses; when left and right initial-link pecks respectively produced terminal links A and B in one component, they produced B and A in the other. Even as the baselines fluctuated, preference was observable within sessions as the difference between relative initial-link response rates in the two components. The first experiment demonstrated the rapid development of preferences when terminal links A and B consisted of fixed-interval 15-s and 30-s schedules. The second demonstrated the sensitivity of the procedure to preference for a fixed-interval 30-s schedule operating for pecks on either of two keys (free choice) over its operating for pecks on only a single key (forced choice).