SQAB 2005: complexity and generalizability.
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Animals↗
Biomedical subjects
Randolph C Grace
Publications and source records attributed to Randolph C Grace.
Choice and timing in concurrent chains: effects of initial-link duration.
Theories of timing have been applied to choice between delayed rewards by assuming that delays are represented in memory and that subjects sample from memory when choosing between alternatives. To search for covariation in single-trial measures of performance that might confirm this assumption, we used a procedure that allowed for convergent measurement of choice and timing behavior. Four pigeons responded in a concurrent chains/peak procedure in which the terminal links were fixed-interval (FI) 8s and FI 16s, across conditions the duration of the initial-link schedule was either short or long, and one quarter of the terminal links lasted for 48 s and ended without reinforcer delivery. Preference for the FI 8-s alternative was stronger with shorter initial links, replicating the 'initial-link effect'. Responding on no-food trials was unaffected by initial-link duration, and aggregated across trials, was typical of the peak procedure: response distributions were approximately Gaussian, with modes near the FI schedule durations, and variance was greater for the FI 16-s terminal link. Analysis of local measures of initial-link performance (e.g., pause to begin responding, time spent responding, number and duration of visits to each alternative, etc.) found that the initial-link effect was associated with an increase in the number and duration of visits per cycle to the nonpreferred alternative. Regression analyses showed that local initial-link measures contributed relatively little additional variance in predicting performance on individual no-food trials beyond that accounted for by FI schedule. Our results provide no clear evidence that initial- and terminal-link responding in concurrent chains are mediated by a common representation of terminal-link delays.
Analysis of Variance↗
Rapid acquisition in concurrent chains: evidence for a decision model.
Pigeons' choice in concurrent chains can adapt to rapidly changing contingencies. Grace, Bragason, and McLean (2003) found that relative initial-link response rate was sensitive to the immediacy ratio in the current session when one of the terminal-link fixed-interval schedules was changed daily according to a pseudorandom binary sequence (e.g., Schofield & Davison, 1997). The present experiment tested whether the degree of variation in delays across sessions had any effect on acquisition rate in Grace et al.'s (2003) rapid-acquisition procedure. In one condition ("minimal variation"), the left terminal link was always fixed-interval 8 s and the right terminal link was either fixed-interval 4 s or fixed-interval 16 s. In the other condition ("maximal variation"), a unique pair of fixed-interval values was used in each session. Responding was sensitive to the current-session immediacy ratio in both conditions, but across subjects there was no systematic difference in sensitivity. These results challenge the view that initial-link responding in the rapid-acquisition procedure is determined by changes in the learned value of the terminal-link stimuli, and suggests instead that a process resembling categorical discrimination may control performance. A decision model based on the assumption that delays are categorized as short or long relative to the history of delays provided a good account of the data and shows promise in being able to explain other choice phenomena.
Animals↗
Initial-link duration and acquisition of preference in concurrent chains.
Initial-link response allocation in concurrent chains becomes less extreme as the absolute duration of the initial links increases (Fantino, 1969). The present study asked whether initial-link duration affected how quickly response allocation reached asymptote (i.e., acquisition of preference). Six pigeons were trained on a concurrent-chains procedure in which the terminal links were fixed-interval (FI) 8 sec FI 16 sec or FI 16 sec FI 8 sec and were reversed every 20 sessions. Across conditions, all possible combinations of transitions between variable-interval (VI) 8-sec (short) and VI 24-sec (long) initial-link schedules were studied. Overall, the rate of acquisition was faster when the durations of the initial links preceding the reversal were short rather than long, and when the durations of the initial links following the reversal were long rather than short. By contrast, initial-link duration had no effect on acquisition or asymptotic measures of temporal control of terminal-link responding. These results support the core principle of delay-reduction theory (Fantino, 1969) that the impact of a conditioned reinforcer varies directly with initial-link duration, but also suggest that temporal learning during the terminal links proceeds independently ofinitial-link duration.
Animals↗
SQAB 2004: finding the center.
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Behavior↗
Resistance to extinction in the steady state and in transition.
Three experiments with pigeons explored the constancy of reinforcer omission during extinction conjectured by rate estimation theory. Experiment 1 arranged 3-component multiple variable-interval (VI) schedules with a mixture of food and extinction trials within each session. Reinforcers omitted to an extinction criterion increased with food-trial reinforcer rate. Experiment 2 arranged 3-component multiple VI schedules where components differed in rate or number of reinforcers. Resistance to extinction depended on the training reinforcer rate but not on the number of reinforcers omitted. Experiment 3 replicated the partial-reinforcement extinction effect within subjects in a discrete-trial procedure and found that more reinforcers were omitted in continuous- than in partial-reinforcement trials. A model of extinction based on behavioral momentum theory accounted for all the data.
Animals↗
Does sensitivity to magnitude depend on the temporal distribution of reinforcement?
Our research addressed the question of whether sensitivity to relative reinforcer magnitude in concurrent chains depends on the distribution of reinforcer delays when the terminal-link schedules are equal. In Experiment 1, 12 pigeons responded in a two-component procedure. In both components, the initial links were concurrent variable-interval 40-s variable-interval 40-s, and the terminal links were both 20-s interval schedules in which responses were reinforced by either 4-s of grain in one, or 2-s of grain in the other. The only difference between the components was whether the terminal-link schedules were fixed interval or variable intervals. For all subjects, the relative rate of responding in the initial links for the terminal link that produced the 4-s reinforcer was greater when the terminal links were fixed-interval schedules than when they were variable-interval schedules. This result is contrary to the prediction of Grace's (1994) contextual choice model, but is consistent with both Mazur's (2001) hyperbolic value-added model and Killeen's (1985) incentive theory. In Experiment 2, 4 pigeons responded in a concurrent-chains procedure in which 4-s or 2-s reinforcers were provided independently of responding according to equal fixed-time or mixed-time schedules. Preference for the 4-s reinforcer increased as the variability of the intervals comprising the mixed-time schedules was decreased. Generalized-matching sensitivity of initial-link response allocation to relative reinforcer magnitude was proportional to the geometric mean of the terminal-link delays.
Animals↗
Integrated versus segregated accounting and the magnitude effect in temporal discounting.
Temporal discounting rates in humans generally decrease as the amount of reward increases, a phenomenon known as the magnitude effect. In the present study, we examined whether temporal discounting and the magnitude effect are related to segregation of choices in terms of gains or losses for waiting for or expediting receipt of a reward. Subjects (N = 24) responded to a series of hypothetical choices about amounts of money available either immediately or after a delay. The immediate and delayed amounts either were presented as integrated amounts in the baseline condition or were segregated as differential gains or losses for choosing delayed or expedited consumption (delay and speedup conditions, respectively). Temporal discounting rates decreased in the segregated conditions, in accord with the standard discounted utility model but contrary to the hypothesis that the subjects were choosing on the basis of reward differentials in the baseline condition. The size of the magnitude effect was comparable in the baseline and the delay conditions but decreased in the speed-up condition. These results challenge explanations of the magnitude effect in terms of an increasing proportional sensitivity property of the utility function (Loewenstein & Prelec, 1992) and the hypothesis that subjects choose on the basis of differentials even when the rewards are presented as integrated amounts.
Accounting↗
Does the terminal-link effect depend on duration or reinforcement rate?
Preference in concurrent chains for the richer terminal-link schedule becomes more extreme as the schedule values increase with their ratio held constant, a result known as the terminal-link effect. We report two experiments that attempt to determine whether this effect is related to terminal-link duration or the overall rate of reinforcement. These variables have been confounded in prior studies, but can be separated by comparing variable-duration schedules that end after a single reinforcer has been earned, with constant-duration schedules during which a variable number of reinforcers may be earned. In Experiment 1, the terminal-link effect was obtained with variable-duration schedules when duration and overall reinforcement rate were manipulated, but not with constant-duration schedules when overall reinforcement rate was changed with duration held constant. In Experiment 2, the terminal-link effect was obtained with constant-duration schedules when duration was manipulated with overall reinforcement rate held constant. Taken together, these results show that the terminal-link effect depends on changes in terminal-link duration, not overall reinforcement rate (or equivalently, average time to reinforcement). This accords with the account of the terminal-link effect provided by the contextual choice model [J. Exp. Anal. Behav. 61 (1994) 113] but not delay-reduction theory [J. Exp. Anal. Behav. 12 (1969) 723].
Animals↗
Temporal context in concurrent chains: I. Terminal-link duration.
Two experiments are reported in which the ratio of the average times spent in the terminal and initial links (Tt/Ti) in concurrent chains was varied. In Experiment 1, pigeons responded in a three-component procedure in which terminal-link variable-interval schedules were in constant ratio, but their average duration increased across components by a factor of two. The log initial-link response ratio was a negatively accelerated function of Tt/Ti. Overall, the data were well described by Grace's (1994) contextual choice model (CCM) with temporal context represented as (Tt/Ti)k or 2Tt/(Tt + Ti), and by Mazur's (2001) hyperbolic value-added model (HVA), with each model accounting for approximately 93% of the variance. In Experiment 2, fixed-parameter predictions for each model were generated, based on the data from Experiment 1, for conditions in which Tt/Ti was varied over a more extreme range. Data were consistent with the predictions of CCM with temporal context represented as 2Tt/(Tt + Ti) and to a lesser extent as (Tt/Ti)k, but not with HVA. Overall, these results suggest that preference increases as a hyperbolic function of Tt/Ti when terminal-link duration is increased relative to initial-link duration, with the terminal-link schedule ratio held constant.
Animals↗
Independence of terminal-link entry rate and immediacy in concurrent chains.
In Phase 1, 4 pigeons were trained on a three-component multiple concurrent-chains procedure in which components differed only in terms of relative terminal-link entry rate. The terminal links were variable-interval schedules and were varied across four conditions to produce immediacy ratios of 4:1, 1:4, 2:1, and 1:2. Relative terminal-link entry rate and relative immediacy had additive and independent effects on initial-link response allocation, and the data were well-described by a generalized-matching model. Regression analyses showed that allowing sensitivity to immediacy to vary across components produced only trivial increases in variance accounted for. Phase 2 used a three-component concurrent-schedules procedure in which the schedules were the same as the initial links of Phase 1. Across two conditions, the relative reinforcer magnitude was varied. Sensitivity to relative reinforcer rate was independent of relative magnitude, confirming results of prior studies. Sensitivity to relative reinforcer rate in Phase 2 did not vary systematically across subjects compared to sensitivity to relative entry rate in Phase 1, and regression analyses confirmed again that only small increases in variance accounted for were obtained when sensitivities were estimated independently compared with a single estimate for both phases. Overall, the data suggest that conditioned and primary reinforcers have functionally equivalent effects on choice and support the independence of relative terminal-link entry rate and immediacy as determiners of response allocation. These results are consistent with current models for concurrent chains, including Grace's (1994) contextual choice model and Mazur's (2001) hyperbolic value-added model.
Animals↗
Rapid acquisition of preference in concurrent chains.
We report two experiments using a concurrent-chains procedure in which one terminal-link schedule was fixed-interval 8 s and the alternative schedule changed randomly from day to day. In Experiment 1, the alternative schedule varied between 4 s and 16 s according to a pseudorandom binary sequence similar to the one used by Hunter and Davison (1985). Similar to results with concurrent schedules, pigeons' response allocation in the initial link was most sensitive to the schedules arranged in the current session, although some effect of prior history was evident. Overall sensitivity was lower than for comparable data from steady-state research. In Experiment 2, a unique value between 2 s and 32 s was used for the alternative-schedule delay in each session. Sensitivity levels were similar to Experiment 1 and remained unchanged across 61 sessions of training. For all subjects, sensitivity was greater when the alternative-schedule delay was greater than 8 s compared with when it was less than 8 s. Generalized-matching plots revealed evidence of clustering of data points into two groups for some pigeons, suggesting that a process similar to a categorical discrimination may have at least partly determined response allocation. Overall, this research shows that pigeons' initial-link response allocation can adjust rapidly to frequent changes in the terminal links.
Animals↗
Preference and resistance to change with constant- and variable-duration terminal links: independence of reinforcement rate and magnitude.
Pigeons responded in a three-component multiple concurrent-chains procedure in which the variable-interval reinforcement schedules were the same across components but magnitudes differed across components. The terminal links were arranged either as a variable delay followed by presentation of a reinforcer ("variable duration") or as a fixed period of access to the schedule during which a variable number of reinforcers could be earned ("constant duration"). Relative reinforcement rate was varied parametrically across both types of conditions. After baseline training in each condition, resistance to change of terminal-link responding was assessed by delivering food during the initial links according to a variable-time schedule. Both preference and resistance to change were more sensitive to reinforcement-rate differences in the constant-duration conditions. Sensitivities of preference and resistance to change to relative reinforcement rate did not change depending on relative reinforcement magnitude. Taken together, these results confirm and extend those of prior studies, and suggest that reinforcement rate and magnitude combine additively to determine preference and resistance to change. A single structural relation linking preference and resistance to change describes all the data from this and several related studies.
Animals↗
The value hypothesis and acquisition of preference in concurrent chains.
Experiment 1 compared the acquisition of initial- and terminal-link responding in concurrent chains. The terminal-link schedules were fixed interval (FI) 10 sec and FI 20 sec, but some presentations were analogous to no-food trials in the peak procedure, lasting 60 sec with no reinforcement delivery. Pigeons completed a series of reversals in which the schedules signaled by the terminal-link stimuli (red and green on the center key) were changed. Acquisition of temporal control of terminal-link responding (as measured by peak location on no-food trials) was more rapid than acquisition of preference in the initial links. Experiment 2 compared acquisition in concurrent chains, using the typical procedure in which the terminal-link schedules are changed with a novel arrangement in which the initial-link key assignments were changed while the terminal-link schedules remained the same. Acquisition of preference was faster in the latter condition, in which the terminal-link stimulus-reinforcer relations were preserved. These experiments provide the first acquisition data that support the view that initial-link preference is determined by the values of the terminal-link stimuli.
Animals↗
Acquisition of preference in concurrent chains: comparing linear-operator and memory-representational models.
Two experiments were conducted to test predictions of 2 models for acquisition of preference in concurrent chains. Pigeons were trained with pairs of fixed-interval and variable-interval terminal-link schedules in a successive-reversal design. Results showed that acquisition rate was faster when fixed-interval schedules preceded and when variable-interval schedules followed the reversal and was approximately constant when the same pair of schedules was used. These results were predicted by both linear-operator and memory-representational models. However, only the linear-operator model predicted effects of schedule duration. Overall, these results demonstrated that a simple linear-operator model can account for the major features of preference acquisition in concurrent chains and suggest that choice in transition and steady state may provide convergent validation of a single delay-discounting function.
Animals↗
Violations of transitivity: Implications for a theory of contextual choice.
Violations of strong stochastic transitivity in concurrent-chains choice were first reported by Navarick and Fantino. In a series of articles, Navarick and Fantino concluded that neither a unidimensional model capable of predicting exact choice probabilities nor a fixed-variable equivalence rule was possible for the concurrent-chains procedure. I show that when choice is modeled contextually (i.e., when preference for a schedule is affected by factors other than the schedule itself, e.g., aspects of the alternative schedule), a unidimensional, exact-choice probability model is possible that both predicts the intransitivities reported by Navarick and Fantino and provides a fixed-variable equivalence rule for the concurrent-chains procedure. The contextual model is an extension of the generalized matching law and violates a key assumption underlying traditional choice models-simple scalability-because of (a) schedule interdependence and (b) bias from procedural contingencies. Therefore, strong stochastic transitivity cannot be expected to hold. Contextual scalability is analyzed to reveal a hierarchy of context effects in choice. Navarick and Fantino's intransitivities can be satisfactorily explained by bias. If attribute sensitivity is context dependent, however, and if there are similarity structures among choice alternatives, the contextual model is shown to be able to predict violations of ordinal preference. Therefore, it may be possible to formulate a deterministic, general psychophysical model of choice as a behavioral alternative to probabilistic, multidimensional choice theories.
Journal Article↗