Bias and sensitivity to reinforcement in a concurrent-chain schedule

Six pigeons were trained on concurrent-chain schedules in which the initial links were either dependent (Experiment 1) or independent (Experiment 2) concurrent variable-interval schedules and the terminal links were fixed-duration delays to reinforcement in blackout. A changeover delay of three seconds operated in the initial links. Both the initial- and terminal-link schedule values were varied over 61 experimental conditions. An analysis of the data using the generalized matching law showed that the sensitivity of initial-link response allocation to the frequency of terminal-link production was independent of both the duration of the terminal-link delays and, though less clearly, of the duration of the initial-link schedules. Sensitivity of initial-link response allocation to terminal-link reinforcer-rate ratios was a joint function of the terminal-link durations and the smaller average initial-link duration. The results showed that the generalized matching law is useful in analyzing concurrent-chain schedule performance and that a changeover delay in the initial links eliminates some terminal- to initial-link interactions that have made quantitative predictions for concurrent-chain performances difficult.     

Stimuli, reinforcers, and behavior: an integration

We propose that a fundamental unit of behavior is the concurrent discriminated operant, and we discuss in detail a quantitative model of the concurrent three-term contingency that is based on the notion that an animal's behavior is controlled to differing extents by both stimulus—behavior and behavior—reinforcer relations. We show how this model can describe performance in a variety of experimental procedures: conditional discrimination and matching to sample, both with and without reinforcement for responses that are traditionally identified as errors; conditional discrimination with more than two stimuli and choice alternatives; delayed matching to sample and delayed reinforcement in matching to sample; second-order and complex conditional discrimination; and multiple and concurrent schedules. Although the model is incomplete in its coverage, and may be incorrect, we believe that this conceptual approach will bear fruit in the development of behavior theory.     

Effects of varying stimulus disparity and the reinforcer ratio in concurrent-schedule and signal-detection procedures.

The present study measured the effects of stimulus and reinforcer variations on pigeons' behavior in two different choice procedures. Two intensities of white light were presented as the stimuli on the main key in a switching-key concurrent schedule and as the sample stimuli in a signal-detection procedure. Under both procedures, the scheduled rate of reinforcement was varied across conditions to produce various ratios of obtained reinforcement. These ratios were obtained for seven pairs of light intensities. In the concurrent schedules, the effects of reinforcer-ratio variations were positively correlated with the physical disparity between the two light intensities. In the signal-detection procedure, changes in the reinforcer ratio produced greater effects on performance when stimulus disparity was very low or very high compared to those found at intermediate levels of stimulus disparity. This discrepancy creates a dilemma for existing behavioral models of signal-detection performance.     

Preference for fixed-interval schedules: effects of initial-link length

Six homing pigeons were trained on a variety of concurrent-chains schedules in which the initial links were equal variable-interval schedules and the terminal links were fixed-interval schedules. Both terminal-link and initial-link schedules were systematically varied. The results showed that preference for a particular terminal-link schedule combination was greater, the shorter the initial-link schedules. The data closely matched predictions from the model of choice suggested by Davison and Temple (1973), but did not match predictions from two other models. An alternative method for analyzing concurrent-chains performance by assuming that the schedule consists of both chained schedules and successive, discriminated components that comprise multiple schedules, was suggested.     

External analyses of preference models

Using Carroll's external analysis, several studies have found that unfolding models account for more, although seldom significantly more, variance in preferences than Tucker's vector model. In studies of sociometric ratings and political preferences, the unfolding model again rarely outpredicted the vector model by a significant amount. Yet on cross-validation, the unfolding model consistently accounted for more variance. Results suggest that sometimes significance tests are less sensitive than cross-validation procedures to the small but consistent superiority of the unfolding model. Future researchers may wish to use significance tests and cross-validation techniques in comparing models.     

Performance in concurrent interval schedules

Four pigeons were trained under concurrent variable-interval variable-interval and fixed-interval variable-interval schedules in a two-key situation. Both response allocation and time allocation to the two schedules were measured when various reinforcement rates were arranged on each key. All animals showed an approximately constant proportional preference for the variable-interval schedule over the fixed-interval schedule. These results support Schneider's (1969) analysis of fixed-interval schedule performance.     

On a metric,unidimensional unfolding model for attitudinal and developmental data

If stimulus responses are linearly related to squared distances between stimulus scale values and person scores along a latent continuum, (a) the stimulus × stimulus correlation matrix will display a simplex-like pattern, (b) the signs of first-order partial correlations can be specified in an empirically testable manner, and (c) the variables will have a semicircular, two-factor structure. Along the semicircle, variables will be ordered by their positions on the latent dimension. The above results suggest procedures for examining the appropriateness of the model and procedures for ordering the stimuli. Applications to developmental and attitudinal data are discussed. This research was supported by a grant from the Graduate School of the University of Minnesota to the author and by a grant from the U. S. Public Health Service (Grant No. 1-R01-MH27861-01) to Dr. James Rest, Principal Investigator.