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.     

On muthén’s maximum likelihood for two-level covariance structure models

Data in social and behavioral sciences are often hierarchically organized. Special statistical procedures that take into account the dependence of such observations have been developed. Among procedures for 2-level covariance structure analysis, Muthén’s maximum likelihood (MUML) has the advantage of easier computation and faster convergence. When data are balanced, MUML is equivalent to the maximum likelihood procedure. Simulation results in the literature endorse the MUML procedure also for unbalanced data. This paper studies the analytical properties of the MUML procedure in general. The results indicate that the MUML procedure leads to correct model inference asymptotically when level-2 sample size goes to infinity and the coefficient of variation of the level-1 sample sizes goes to zero. The study clearly identifies the impact of level-1 and level-2 sample sizes on the standard errors and test statistic of the MUML procedure. Analytical results explain previous simulation results and will guide the design or data collection for the future applications of MUML.This research was supported by NSF Grant DMS04-37167.We thank Dr.Bengt Muthén for providing key references. We are also grateful to three expert reviewers for their constructive comments that have led the paper to an improvement over the previous version.This revised article was published online in August 2005 with the PDF paginated correctly.     

Dynamics of the dyad: How mothers and infants co-construct interaction spaces during object play

Studies of dyadic interaction often examine infants’ social exchanges with their caregivers in settings that constrain their physical properties (e.g., infant posture, fixed seating location for infants and adults). Methodological decisions about the physical arrangements of interaction, however, may limit our ability to understand how posture and position shape them. Here we focused on these embodied properties of dyadic interaction in the context of object play. We followed 30 mother–infant dyads across the first year of life (at 3, 6, 9, and 12 months) and observed them during 5 min of play with a standard set of toys. Using an interval-based coding system, we measured developmental change in infant posture, how mothers and infants positioned themselves relative to one another, and how they populated interaction spaces with objects. Results showed that mother–infant dyads co-constructed interaction spaces and that the contributions of each partner changed across development. Dyads progressively adopted a broader spatial co-orientation during play (e.g., positioned at right angles) across the first year. Moreover, advances in infants’ postural skills, particularly increases in the use of independent sitting in real time, uniquely predicted change in dyadic co-orientation and infants’ actions with objects, independent of age. Taken together, we show that the embodied properties of dyadic object play help determine how interactions are physically organized and unfold, both in real time and across the first year of life.     

Reinforcer efficacy in a delayed matching-to-sample task.

Five domestic hens were exposed to a delayed matching-to-sample task. Conditions 1, 5, and 8 were variable-delay conditions in which five delays (0.25, 1, 2, 4, and 8 s) from the red or green sample to the presentation of the red and green comparison stimuli were presented a number of times during each session. In the fixed-delay condition (Condition 3), each delay was presented for 15 sessions under a Latin square design across birds. When improvements in accuracy across the variable-delay conditions are taken into account, the data were similar under both the variable and fixed delays. In Conditions 2, 4, 6, and 7 sample-reinforcer intervals were held at 8, 8, 4, and 2 s, respectively, while sample-choice intervals were varied within these during each session. With increasing sample-reinforcer interval, both initial discriminability (i.e., with sample-choice delay = 0) and rate of decrement in discriminability decreased. Although the former would be predicted if accuracy depends of the average sample-reinforcer interval, the latter would not. These data show that increasing the sample-choice interval had less effect on matching accuracy than increasing the sample-reinforcer interval did.     

Investigating Behavioral Dynamics With A Fixed-time Extinction Schedule And Linear Analysis

This paper describes the behavioral adaptation observed for 16 pigeons responding to a step transition in the reinforcement rate in a repeated-trial design. Within each trial, following exposure for a fixed period to a variable-interval schedule, there was an unsignaled change in the schedule to extinction. The step transition allowed an experimental test of the applicability of a linear analysis to steady-state dynamic behavior. The computations required for this test yielded, as an intermediate result, transfer functions for each of the 16 birds from 1 mHz to 256 mHz. The transfer functions obtained show greater responsiveness to lower frequencies (i.e., longer time-scale structures in the reinforcement schedule); hence, the pigeons have the characteristics of a low-pass filter. The outcome of the test is that some predictability of the pigeons' future behavior is possible.     

Dynamics of time discrimination: II. The effects of multiple impulses.

According to a diffusion generalization model, time discrimination is determined by the frequency and recency of preceding intervals of time. A procedure for studying rapid timing was used to investigate whether pigeons' wait-time responses were sensitive to these factors. In Experiment 1 the number (two or eight) and spacing (consecutive or far apart) of 5-s interfood intervals (called impulses) intercalated in a series of 15-s interfood intervals (nonimpulses) were studied. Experiment 2 was identical to the first but the interfood intervals were increased by a factor of three. Overall, impulses shortened wait times in the next interfood interval. However, several impulses occurring in succession extended the localized effect of an impulse: Wait times following a set of eight-close impulses were slow to recover to preimpulse levels. The results show that linear waiting is only an approximation to the dynamic process, and a process that is sensitive to events in an animal's remote past, such as the diffusion generalization model, provides a better account of rapid timing effects.     

Psychological distance to reward: Segmentation of aperiodic schedules of reinforcement

College students responded for monetary rewards in two experiments on choice between differentially segmented aperiodic schedules of reinforcement. On a microcomputer, the concurrent chains were simulated as an air-defense video game in which subjects used two radars for detecting and destroying enemy aircraft. To earn more cash-exchangeable points, subjects had to shoot down as many planes as possible within a given period of time. For both experiments, access to one of two radar systems (terminal link) was controlled by a pair of independent concurrent variable-interval 60-s schedules (initial link) with a 4-s changeover delay always in effect. In Experiment 1, the appearance of an enemy aircraft in the terminal link was determined by a variable-interval (15 s or 60 s) schedule or a two-component chained variable-interval schedule of equal duration. Experiment 2 was similar to Experiment 1 except for the segmented schedule, which had three components. Subjects preferred the unsegmented schedule over its segmented counterpart in the conditions with variable-interval 60 s, and preference tended to be more pronounced with more components in the segmented schedule. These findings are compatible with those from previous studies of periodic and aperiodic schedules with pigeons or humans as subjects.     

Pigeons' wait-time responses to transitions in interfood-interval duration: Another look at cyclic schedule performance

Recent developments reveal that animals can rapidly learn about intervals of time. We studied the nature of this fast-acting process in two experiments. In Experiment 1 pigeons were exposed to a modified fixed-time schedule, in which the time between food rewards (interfood interval) changed at an unpredictable point in each session, either decreasing from 15 to 5 s (step-down) or increasing from 15 to 45 s (step-up). The birds were able to track under both conditions by producing postreinforcement wait times proportional to the preceding interfood-interval duration. However, the time course of responding differed: Tracking was apparently more gradual in the step-up condition. Experiment 2 studied the effect of having both kinds of transitions within the same session by exposing pigeons to a repeating (cyclic) sequence of the interfood-interval values used in Experiment 1. Pigeons detected changes in the input sequence of interfood intervals, but only for a few sessions—discrimination worsened with further training. The dynamic effects we observed do not support a linear waiting process of time discrimination, but instead point to a timing mechanism based on the frequency and recency of prior interfood intervals and not the preceding interfood interval alone.