DYNAMIC RESPONSE-BY-RESPONSE MODELS OF MATCHING BEHAVIOR IN RHESUS MONKEYS
Open accessAbstract
We studied the choice behavior of 2 monkeys in a discrete-trial task with reinforcement contingencies similar to those Herrnstein (1961) used when he described the matching law. In each session, the monkeys experienced blocks of discrete trials at different relative-reinforcer frequencies or magnitudes with unsignalled transitions between the blocks. Steady-state data following adjustment to each transition were well characterized by the generalized matching law; response ratios undermatched reinforcer frequency ratios but matched reinforcer magnitude ratios. We modelled response-by-response behavior with linear models that used past reinforcers as well as past choices to predict the monkeys' choices on each trial. We found that more recently obtained reinforcers more strongly influenced choice behavior. Perhaps surprisingly, we also found that the monkeys' actions were influenced by the pattern of their own past choices. It was necessary to incorporate both past reinforcers and past choices in order to accurately capture steady-state behavior as well as the fluctuations during block transitions and the response-by-response patterns of behavior. Our results suggest that simple reinforcement learning models must account for the effects of past choices to accurately characterize behavior in this task, and that models with these properties provide a conceptual tool for studying how both past reinforcers and past choices are integrated by the neural systems that generate behavior.
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Written from the paper’s full text.
TL;DR
In a discrete-trial matching task with unsignalled within-session changes in reinforcer frequency or magnitude, two rhesus monkeys’ steady-state choices were well described by the generalized matching law, but response-by-response choices required a model that included both past reinforcers and past choices. The best-fitting logistic models used local histories and revealed decaying reinforcer effects plus choice-history effects that produce fix-and-sample behavior.
Key findings
- Steady-state behavior was well fit by the generalized matching law, accounting for 90% of the variance for both monkeys. Frequency conditions showed undermatching (pooled sensitivity to reinforcer frequency: Monkey H a = 0.51, SE 0.01; Monkey B a = 0.54, SE 0.01), whereas magnitude conditions showed matching or slight overmatching (pooled sensitivity to reinforcer magnitude: Monkey H b = 1.00, SE 0.02; Monkey B b = 1.22, SE 0.04).
- After unsignalled block transitions, monkeys reached 50% choice of the richer alternative in 11.4 trials (Monkey H) and 10.42 trials (Monkey B) for frequency conditions, and 11.56 trials (Monkey H) and 10.86 trials (Monkey B) for magnitude conditions. In magnitude conditions, transitions to a 3:1 ratio were faster (9.84 and 8.55 trials) than transitions to a 3:2 ratio (13.27 and 13.17 trials).
- Runlengths for the nonpreferred alternative were typically one trial (mean 1.05 trials, SD 0.09), rejecting a purely probabilistic independent-choice model and showing a fix-and-sample pattern.
- The best response-by-response models included both past reinforcers and past choices, integrating on average 14 past reinforcers and 22 past choices. More recent reinforcers more strongly influenced choice; past choices showed a negative coefficient for the last trial (alternation tendency) and positive coefficients for earlier trials (persistence tendency). Residual autocorrelations were mostly within 95% confidence intervals, while a model with only reinforcer history was inadequate.
Methods
- Two male rhesus monkeys performed a discrete-trial two-alternative eye-movement choice task with water reinforcement. Reinforcers were arranged by independent biased-coin arming probabilities with hold, without a changeover delay; within sessions, unsignalled blocks varied relative reinforcer frequency or magnitude.
- Data were 67,827 completed trials from Monkey H and 47,160 from Monkey B, collected after at least 3 months of training; aborted trials were excluded (7% for Monkey H, 6% for Monkey B).
- Steady-state data from the last 65 trials of each block were fit with the generalized matching law. Response-by-response choice was modeled with logistic regression using past reinforcers and past choices, with AIC selecting history lengths up to 50 trials; residual autocorrelation assessed model fit.
Limitations
- The paper states the statistical model is principally descriptive, and that between-subject variability precluded determining whether exponential or hyperbolic weighting better describes the reinforcer-history coefficients.
- The paper notes a misprediction: in extreme magnitude transitions, the monkeys adjusted faster than the model predicted.
- Evident from the text: only two male rhesus monkeys were studied, so generality is limited; no formal sample-size limitation is stated in the paper.
Model-written summary. Check it against the paper before relying on it.
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Claims the paper makes
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- Findingown data§ Results
The coefficients and quality of fits of the generalized matching law were similar for the 2 monkeys.
“The coefficients and quality of fits were similar for the 2 monkeys, consistent with the examples shown in Figure 3.”
Quote in the paperNot a substantial claim - Findingown data§ Results
Following acquisition, the animals' behavior fluctuated about a steady-state.
“Figure 2 shows that there was a period following acquisition where the animals' behavior fluctuated about a steady-state.”
Quote in the paperSubstantial claim - Findingown data§ Abstract
Response ratios matched reinforcer magnitude ratios.
“Steady-state data following adjustment to each transition were well characterized by the generalized matching law; response ratios undermatched reinforcer frequency ratios but matched reinforcer magnitude ratios.”
Quote in the paperSubstantial claim - Findingown data§ Abstract
Response ratios undermatched reinforcer frequency ratios.
“Steady-state data following adjustment to each transition were well characterized by the generalized matching law; response ratios undermatched reinforcer frequency ratios but matched reinforcer magnitude ratios.”
Quote in the paperSubstantial claim - Findingown data§ Results
Both animals showed greater sensitivity to reinforcer magnitude (b) than reinforcer frequency (a).
“Both animals showed greater sensitivity to reinforcer magnitude (b) than reinforcer frequency (a).”
Quote in the paperSubstantial claim
- Findingown data§ Results
There was no difference between the acquisition times for the two possible posttransition ratios in each frequency condition (~3:1 and ~6:1).
“There was no difference between the acquisition times for the two possible posttransition ratios in each condition (∼3∶1 and ∼6∶1).”
Quote in the paperNot a substantial claim - Findingown data§ Abstract
Accounting for recent choices also is required for accurate predictions by models of this type.
“but we extend this to show that accounting for recent choices also is required for accurate predictions by models of this type.”
Quote in the paperSubstantial claim - Findingown data§ Results
The acquisition time averaged 11.56 trials for Monkey H and 10.86 trials for Monkey B over all conditions where reinforcer magnitude was manipulated.
“The acquisition time was 11.56 trials for Monkey H and 10.86 trials for Monkey B averaged over all the conditions where reinforcer magnitude was manipulated.”
Quote in the paperNot a substantial claim - Findingown data§ Results
The number of trials to reach a 50% rate of choosing the richer alternative following a block transition averaged 11.4 trials for Monkey H and 10.42 trials for Monkey B over all conditions where reinforcer frequency was manipulated.
“This was 11.4 trials for Monkey H and 10.42 trials for Monkey B averaged over all the conditions where reinforcer frequency was manipulated.”
Quote in the paperNot a substantial claim - Findingown data§ Abstract
The monkeys' actions were influenced by the pattern of their own past choices.
“Perhaps surprisingly, we also found that the monkeys' actions were influenced by the pattern of their own past choices.”
Quote in the paperSubstantial claim - Findingown data§ Results
For the reinforcer magnitude conditions, transitions to a 3:1 ratio were faster (9.84 trials for Monkey H and 8.55 trials for Monkey B) than transitions to a 3:2 ratio (13.27 trials for Monkey H and 13.17 trials for Monkey B).
“transitions to a 3∶1 ratio were faster (9.84 trials for Monkey H and 8.55 trials for Monkey B) than transitions to a 3∶2 ratio (13.27 trials for Monkey H and 13.17 trials for Monkey B).”
Quote in the paperSubstantial claim - Findingown data§ Abstract
More recently obtained reinforcers more strongly influenced choice behavior.
“We found that more recently obtained reinforcers more strongly influenced choice behavior.”
Quote in the paperSubstantial claim - Findingown data§ Abstract
Steady-state data following adjustment to each transition were well characterized by the generalized matching law.
“Steady-state data following adjustment to each transition were well characterized by the generalized matching law; response ratios undermatched reinforcer frequency ratios but matched reinforcer magnitude ratios.”
- Also stated in: § Results · boosted
“The generalized matching law provided good fits to the data, accounting for 90% of the variance in the data for both monkeys.”
Quote in the paperSubstantial claim - Also stated in: § Results · boosted
- Findingown data§ Results
The generalized matching law provided good fits to the data, accounting for 90% of the variance in the data for both monkeys.
“The generalized matching law provided good fits to the data, accounting for 90% of the variance in the data for both monkeys.”
Quote in the paperSubstantial claim - Findingown data§ Abstract
It was necessary to incorporate both past reinforcers and past choices in order to accurately capture steady-state behavior as well as the fluctuations during block transitions and the response-by-response patterns of behavior.
“It was necessary to incorporate both past reinforcers and past choices in order to accurately capture steady-state behavior as well as the fluctuations during block transitions and the response-by-response patterns of behavior.”
Quote in the paperSubstantial claim - Findingown data§ Discussion
When relative frequencies of reinforcement were varied, monkeys preferred the rich alternative less than expected if they strictly matched the ratio of their choices to the ratio of reinforcers obtained, a finding known as undermatching.
“When we varied the relative frequencies of reinforcement, we found that monkeys preferred the rich alternative less than would be expected if they strictly matched the ratio of their choices to the ratio of reinforcers obtained, a finding known as undermatching.”
Quote in the paperSubstantial claim - Findingown data§ Discussion
In the magnitude conditions, both monkeys matched, or slightly overmatched, their choice allocation to the ratio of obtained reinforcers.
“However, in the magnitude conditions we found that both monkeys matched, or slightly overmatched, their choice allocation to the ratio of obtained reinforcers.”
Quote in the paperSubstantial claim - Findingown data§ Results
There is a misprediction in the extreme transitions for the magnitude conditions: the monkeys were quicker to respond to new reinforcer conditions than the model predicted.
“There is a misprediction, however, that is obvious only in the extreme transitions for the magnitude conditions (lower right panel in Figure 8). For these transitions, the monkeys were quicker to respond to new reinforcer conditions than the model predicted.”
Quote in the paperNot a substantial claim - Findingown data§ Discussion
Failure to account for the effects of enough past choices resulted in reinforcer effects that remained significant up to 30 trials into the past.
“In our data, failure to account for the effects of enough past choices resulted in reinforcer effects that remained significant up to 30 trials into the past.”
Quote in the paperSubstantial claim- The authors state this as an assumption: Past reinforcers and choices are linearly combined to determine choice on each trial.
- The authors state this as an assumption: The effects of past reinforcers and choices are symmetric: a past reinforcer or choice to the right changes the odds of choosing right by the same amount that a past reinforcer or choice to the left changes the odds of choosing left.
- Findingown data§ Discussion
Choice behavior during both steady-state periods at the end of each block and rapid shifts during transitions between blocks was well characterized by a response-by-response model that linearly combined past reinforcers and past choices to predict current choice.
“We found that choice behavior during both steady-state periods at the end of each block as well as in the rapid shifts during transitions between blocks were well characterized by a response-by-response model that linearly combined past reinforcers and past choices to predict current choice.”
Quote in the paperSubstantial claim- The authors state this as an assumption: Past reinforcers and choices are linearly combined to determine choice on each trial.
- The authors state this as an assumption: The effects of past reinforcers and choices are symmetric: a past reinforcer or choice to the right changes the odds of choosing right by the same amount that a past reinforcer or choice to the left changes the odds of choosing left.
- Findingown data§ Discussion
There was a decaying effect of past reinforcers, with more recently obtained reinforcers more strongly influencing choice behavior.
“We found a decaying effect of past reinforcers with more recently obtained reinforcers more strongly influencing choice behavior.”
Quote in the paperSubstantial claim- The authors state this as an assumption: Past reinforcers and choices are linearly combined to determine choice on each trial.
- The authors state this as an assumption: The effects of past reinforcers and choices are symmetric: a past reinforcer or choice to the right changes the odds of choosing right by the same amount that a past reinforcer or choice to the left changes the odds of choosing left.
- Findingown data§ Discussion
Even though the monkeys' choice behavior was variable at a response-by-response level, behavior averaged over tens of trials was a lawful function of reinforcer frequency and magnitude.
“We showed that even though the monkeys' choice behavior was variable at a response-by-response level, behavior averaged over tens of trials was a lawful function of reinforcer frequency and magnitude.”
Quote in the paperSubstantial claim - Findingcitation§ Discussion
Steady-state behavior at the end of each block was well accounted for by the generalized matching law.
“Steady-state behavior at the end of each block was well accounted for by the generalized matching law (Baum, 1974).”
Quote in the paperSubstantial claim0 of 1 sources checked- cites Baum, 1974 source
Not checked in the free run.
- Findingown data§ Results
Neither animal exhibited a significant spatial bias.
“Because neither animal exhibited a significant spatial bias, runlengths were compiled for the preferred and nonpreferred alternatives irrespective of spatial location.”
Quote in the paperSubstantial claim - Findingown data§ Discussion
When the effects of past choices were accounted for, the effects of past reinforcers were highly local, becoming essentially ineffective by 5 to 10 trials into the past.
“In our analysis, when the effects of past choices were accounted for, we found that the effects of past reinforcers were highly local, becoming essentially ineffective by the time they have moved 5 to 10 trials into the past (Figure 6).”
Quote in the paperSubstantial claim- The authors state this as an assumption: Past reinforcers and choices are linearly combined to determine choice on each trial.
- The authors state this as an assumption: The effects of past reinforcers and choices are symmetric: a past reinforcer or choice to the right changes the odds of choosing right by the same amount that a past reinforcer or choice to the left changes the odds of choosing left.
- Findingown data§ Results
There was a bias towards the rich alternative that was larger for the magnitude conditions.
“There was, however, a bias towards the rich alternative that was larger for the magnitude conditions.”
Quote in the paperNot a substantial claim - Findingown data§ Discussion
Choice behavior began to shift towards the richer alternative after relatively few reinforcers had been delivered in the new reinforcer conditions, despite block changes being unsignalled and unpredictable.
“Choice behavior began to shift towards the richer alternative after relatively few reinforcers had been delivered in the new reinforcer conditions, despite the fact that block changes were unsignalled and unpredictable.”
Quote in the paperSubstantial claim - Findingown data§ Results
The best models selected by AIC are very local, integrating relatively few past reinforcers (average 14 trials) and choices (average 22 trials).
“The best models are very local, integrating relatively few past reinforcers (average 14 trials) and choices (average 22 trials), which confirms the visual impression provided by Figure 6.”
Quote in the paperSubstantial claim - Findingown data§ Discussion
Monkeys engaged in a choice task appear to integrate both past reinforcers and past choices.
“We have shown that monkeys engaged in a choice task appear to integrate both past reinforcers and past choices.”
Quote in the paperSubstantial claim- The authors state this as an assumption: Animals form internal representations about recently obtained reinforcers.
- Findingown data§ Discussion
Incorporating memory for both past reinforcers and past choices was necessary to account for the structured patterns of choice behavior observed.
“Incorporating memory for both of these elements was necessary to account for the structured patterns of choice behavior we observed.”
Quote in the paperSubstantial claim- The authors state this as an assumption: Animals form internal representations about recently obtained reinforcers.
- Findingown data§ Discussion
Variability between subjects precludes determining which particular form of weighting is more appropriate for the data.
“The variability between subjects precludes determining which particular form of weighting is more appropriate for our data”
Quote in the paperSubstantial claim - Interpretationreasoning§ Abstract
These procedural differences make it difficult to relate monkey choice behavior as described by neuroscientists to the existing literature on the matching law.
“These differences make it difficult to relate monkey choice behavior as described by neuroscientists to the existing literature on the matching law.”
Quote in the paperNot a substantial claim - Interpretationreasoning§ Abstract
Analyses of reinforcer effects or sequential choice effects in isolation may not have a straightforward interpretation.
“This suggests that analyses of reinforcer effects or sequential choice effects in isolation may not have a straightforward interpretation.”
Quote in the paperSubstantial claim - Premisereasoning§ Abstract
This method of arranging reinforcers renders exclusive choice of an alternative suboptimal for maximizing reinforcer rate because at some point the probability of reinforcement of the unchosen alternative exceeds that of the chosen alternative.
“And like concurrent VI VI schedules, this method of arranging reinforcers renders exclusive choice of an alternative suboptimal for maximizing reinforcer rate because at some point the probability of reinforcement of the unchosen alternative exceeds that of the chosen alternative.”
Quote in the paperSubstantial claim - Premisenone given§ Abstract
The generalized matching law does not specify how animals produce matching behavior at a response-by-response level.
“However, the generalized matching law does not specify how animals produce matching behavior at a response-by-response level.”
Quote in the paperSubstantial claim - Premisecitation§ Abstract
Behavioral research that has been done with monkeys differs in a number of procedural details from the behavioral methods used in neuroscience.
“the behavioral research that has been done with monkeys (Anderson, Velkey, & Woolverton, 2002; Iglauer & Woods, 1974) differs in a number of procedural details from the behavioral methods used in neuroscience.”
Quote in the paperSubstantial claim0 of 2 sources checked- cites Anderson, Velkey, & Woolverton, 2002
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- cites Iglauer & Woods, 1974
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- Premisecitation§ Abstract
For tasks like ours, maximizing reinforcer rate is closely approximated when subjects match the proportion of choices allocated to an alternative to the proportion of reinforcers received from choosing it.
“In fact, for tasks like ours, maximizing reinforcer rate is closely approximated when subjects match the proportion of choices allocated to an alternative to the proportion of reinforcers received from choosing it (Houston & McNamara, 1981; Staddon et al., 1981).”
Quote in the paperSubstantial claim0 of 2 sources checked- cites Houston & McNamara, 1981
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- cites Staddon et al., 1981 source
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- Premisecitation§ Abstract
Behavior generally represents some combination of effects due to reinforcers and intrinsic response-by-response patterning of behavior.
“Although it is conceptually useful to separate the effects of reinforcers and the potentially intrinsic response-by-response patterning of behavior (e.g., tendencies to generate particular sequences of behavior), behavior generally represents some combination of these two (Davison, 2004; Heyman, 1979; Palya, 1992).”
Quote in the paperSubstantial claim0 of 3 sources checked - Premisecitation§ Abstract
In the discrete-trial task used, the probability of reinforcement for choosing a particular alternative grows with the number of trials spent not choosing that alternative, similar to the exponential growth obtained with constant-probability VI schedules.
“We used a discrete-trial task where the probability of reinforcement for choosing a particular alternative grows with the number of trials spent not choosing that alternative, similar to the exponential growth obtained with constant-probability VI schedules (e.g., Houston & McNamara, 1981; Staddon, Hinson, & Kram, 1981).”
Quote in the paperSubstantial claim0 of 2 sources checked- cites Houston & McNamara, 1981
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- cites Staddon, Hinson, & Kram, 1981
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- Study design and conductown data§ Results
Behavior had, on average, reached a steady-state by the last 65 trials of each block.
“We chose this number based on plots like Figure 2, which show that behavior had, on average, reached a steady-state by this point in each block.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Abstract
The generalized matching law is less useful for making neurophysiological predictions because it does not constrain how neural activity should vary on a response-by-response basis.
“As such, the generalized matching law is less useful for making neurophysiological predictions because it does not constrain how neural activity should vary on a response-by-response basis.”
Quote in the paperSubstantial claim - Premisecitation§ Abstract
This also is true of concurrent VI VI schedules.
“This also is true of concurrent VI VI schedules (Staddon & Motheral, 1978), and allows us to compare our results with previous work on the matching law.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites Staddon & Motheral, 1978
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- Interpretationown data§ Results
Average preference as specified by the generalized matching law is insufficient to specify the average runlength patterns.
“implying that average preference as specified by the generalized matching law is insufficient to specify the average runlength patterns.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Results
Part of the reason that the effects of past choice extend further into the past than the effects of past reinforcers is that there are many more choices than reinforced choices because subjects were not reinforced on every response, providing more data with which to fit choice history coefficients.
“Part of the reason that the effects of past choice extends further into the past than the effects of past reinforcers is due to the fact that there are many more choices than there are reinforced choices because subjects were not reinforced on every response. This provides more data with which to fit the choice history coefficients.”
Quote in the paperSubstantial claim - Interpretationown data§ Results
Taken together, the analyses suggest that a local linear model that includes an effect for past choices accounted for behavior in the task.
“Taken together, the analyses suggest that a local linear model that includes an effect for past choices accounted for behavior in our task.”
Quote in the paperSubstantial claim - Premisecitation§ Discussion
Like the present study, Anderson et al. (2002) reported strong undermatching in monkeys performing under standard concurrent VI VI schedules for food reinforcers.
“However, like us, Anderson et al. (2002) reported strong undermatching in monkeys performing under standard concurrent VI VI schedules for food reinforcers.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Anderson et al. (2002) source
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- Interpretationcitation§ Discussion
Incorporating choice as a covariate in dynamic response-by-response models allows one to isolate changes due to past choices from those due to past reinforcers.
“Incorporating choice as a covariate in dynamic response-by-response models allows one to isolate these changes from those due to past reinforcers (Lee et al., 2004; Mookherjee & Sopher, 1994).”
Quote in the paperSubstantial claim0 of 2 sources checked- cites Lee et al., 2004 source
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- cites Mookherjee & Sopher, 1994
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- Interpretationown data§ Results
Even though incorporating the effects of past choices into the model increases its complexity, its improved ability to fit the data makes up for the cost of adding these extra parameters.
“Even though incorporating the effects of past choices into the model increases its complexity, its improved ability to fit the data makes up for the cost of adding these extra parameters.”
Quote in the paperSubstantial claim - Premisecitation§ Discussion
Strong undermatching is commonly observed under conditions like frequent or continuous schedule changes.
“Indeed, strong undermatching is commonly observed under conditions like those we used, such as frequent (Davison & Baum, 2000) or continuous (Palya & Allan, 2003) schedule changes.”
Quote in the paperSubstantial claim0 of 2 sources checked- cites Davison & Baum, 2000
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- cites Palya & Allan, 2003
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- Interpretationreasoning§ Results
Taken together, the model coefficients indicate that recent reinforcers and choices act to produce persistence on the rich alternative with occasional sampling of the lean alternative.
“Taken together the model coefficients indicate that recent reinforcers and choices act to produce persistence on the rich alternative with occasional sampling of the lean alternative.”
Quote in the paperSubstantial claim- The authors state this as an assumption: Past reinforcers and choices are linearly combined to determine choice on each trial.
- The authors state this as an assumption: The effects of past reinforcers and choices are symmetric: a past reinforcer or choice to the right changes the odds of choosing right by the same amount that a past reinforcer or choice to the left changes the odds of choosing left.
- Interpretationreasoning§ Discussion
These results show that animals can adjust the degree to which memories of past reinforcers and choices influence behavior.
“These results show that animals can adjust the degree to which memories of past reinforcers and choices influence behavior.”
Quote in the paperSubstantial claim - Interpretationown data§ Results
The runlength analysis shows that the monkeys' choices on individual trials were not independent during steady-state behavior.
“The runlength analysis highlights the fact that the monkeys' choices on individual trials were not independent during steady-state behavior.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Discussion
Combined with the effects of past reinforcers, these tendencies produced a fix-and-sample pattern of choice: a tendency to persist on the rich alternative with brief visits to the lean alternative.
“Combined with the effects of past reinforcers, this produced a fix-and-sample pattern of choice; there was a tendency to persist on the rich alternative with brief visits to the lean alternative.”
Quote in the paperSubstantial claim - Premisecitation§ Discussion
Regarding high sensitivity to magnitude, published data are varied, with observations of near-strict matching as well as undermatching.
“Regarding the high sensitivity to magnitude, the published data are varied, with observations of near-strict matching (Brownstein, 1971; Keller & Gollub, 1977; Neuringer, 1967) as well as undermatching (Schneider, 1973; Todorov, 1973) being reported.”
Quote in the paperNot a substantial claim0 of 3 sources checked - Interpretationreasoning§ Discussion
In the rescaled formulation, past reinforcers are weighted to provide local estimates of the difference in average reinforcer rate from each alternative.
“This equivalent formulation has a simple interpretation; past reinforcers are weighted to provide local estimates of the difference in average reinforcer rate from each alternative.”
Quote in the paperNot a substantial claim - Premisecitation§ Discussion
Models using an exponentially weighted average possess independence-of-path because all knowledge about past reinforcers is represented by a single number.
“This is true for models using an exponentially weighted average because all knowledge about past reinforcers is represented by a single number; this formulation thus possesses an independence-of-path (Bush & Mosteller, 1955; Luce, 1959).”
Quote in the paperNot a substantial claim0 of 2 sources checked- cites Bush & Mosteller, 1955
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- cites Luce, 1959
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- Interpretationcitation§ Discussion
These results indicate that parietal cortex receives information about both sensory and reinforcing aspects of the environment.
“These results indicate that parietal cortex receives information about both sensory and reinforcing aspects of the environment.”
Quote in the paperNot a substantial claim - Interpretationcitation§ Discussion
Behaving optimally in tasks like ours requires counting the number of choices since the last changeover.
“Thus, behaving optimally in tasks like ours requires counting the number of choices since the last changeover.”
Quote in the paperSubstantial claim - Premisecitation§ Discussion
Dorris and Glimcher (2004) and Sugrue et al. (2004) found that activity of parietal cortex neurons was correlated with estimates of value derived by fitting models using reinforcement rate to predict monkeys' behavior.
“They found that the activity of neurons in parietal cortex was correlated with estimates of value derived by fitting models using reinforcement rate to predict the monkeys' behavior (similar to Figure 10, but without taking into account past choices).”
Quote in the paperNot a substantial claim0 of 2 sources checked- cites Dorris and Glimcher (2004)
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- cites Sugrue et al. (2004) source
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- Premisereasoning§ Discussion
None of the models using these decision rules explicitly allows for sequential structure in choice behavior beyond that induced by structure in the obtained reinforcers.
“None of the models using these decision rules explicitly allows for sequential structure in choice behavior beyond that induced by structure in the obtained reinforcers.”
Quote in the paperSubstantial claim - Premisecitation§ Discussion
Empirical tests of the hypothesis that animals use trial counting to maximize reinforcement rate are equivocal, with evidence for and against the hypothesis.
“Empirical tests of the hypothesis that animals use trial counting to maximize reinforcement rate are equivocal, with evidence for (Hinson & Staddon, 1983; Shimp, 1966; Silberberg et al., 1978) and against (Herrnstein, data published in de Villiers, 1977; Heyman, 1979; Nevin, 1969, 1979) the hypothesis.”
Quote in the paperSubstantial claim0 of 3 sources checked- cites Hinson & Staddon, 1983
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- cites Shimp, 1966 source
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- cites Silberberg et al., 1978
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- Interpretationown data§ Discussion
The general shape of the reinforcer coefficients supports the idea that animals represent reinforcement rate using algorithms that approximate linear weightings.
“but the general shape of the reinforcer coefficients supports the idea that animals represent reinforcement rate using algorithms that approximate these linear weightings.”
Quote in the paperSubstantial claim- The authors state this as an assumption: Animals form internal representations about recently obtained reinforcers.
- Premisecitation§ Discussion
Barraclough et al. (2004) present evidence from a repeated-choice task that some neurons in prefrontal cortex encode the identity of the last response, independent of whether the last response was reinforced or not.
“Barraclough et al. (2004) present evidence from a repeated-choice task that some neurons in prefrontal cortex encode the identity of the last response, independent of whether the last response was reinforced or not.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Barraclough et al. (2004) source
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- Premisecitation§ Discussion
Machado (1993) incorporated short-term memory for past responses into his behavioral models.
“Machado (1993) remedied this by incorporating short-term memory for past responses into his behavioral models.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Machado (1993) source
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- May combine two claims. 39
- The quote only partly states this claim. 1
- Classified as probably not a substantial claim. 31
May combine two claims.
Findingown data§ ResultsAdding polynomial covariates for nonlinear transformations of relative reinforcer frequency and magnitude to Equation 2 accounted for quadratic and cubic deviations but increased average variance explained by only 1.8% (range 0.31-3.81%) in the reinforcer frequency conditions and 1.5% (range 0.13-2.63%) in the reinforcer magnitude conditions.
“Including these covariates accounted for quadratic and cubic deviations in the data, but only increased the average percentage of variance explained by 1.8% (range, 0.31 to 3.81%) and 1.5% (range, 0.13 to 2.63%) for the reinforcer frequency and reinforcer magnitude conditions, respectively.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ AbstractLocal linear weightings of past reinforcers predict the choice behavior of monkeys performing a matching task, with weights similar to those suggested by reinforcer rate estimation models.
“We have found that local linear weightings of past reinforcers predict the choice behavior of monkeys performing a matching task, with weights similar to those suggested by reinforcer rate estimation models, but we extend this to show that accounting for recent choices also is required for accurate predictions by models of this type.”
Quote in the paperSubstantial claimMay combine two claims. The quote only partly states this claim.
Findingown data§ ResultsThere was a rapid acquisition period following an unsignalled block transition, and the choice curves diverged for the two possible posttransition ratios.
“There was a rapid acquisition period following the transition, and the curves diverged for the two possible posttransition ratios.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ ResultsFor both monkeys, the coefficients for reinforcer history are similar in shape for the probability and magnitude conditions, although the coefficients are larger in the probability conditions.
“For both monkeys, the coefficients for reinforcer history are similar in shape for both the probability and magnitude conditions, although the coefficients are larger in the probability conditions.”
Quote in the paperNot a substantial claim- The authors state this as an assumption: Past reinforcers and choices are linearly combined to determine choice on each trial.
- The authors state this as an assumption: The effects of past reinforcers and choices are symmetric: a past reinforcer or choice to the right changes the odds of choosing right by the same amount that a past reinforcer or choice to the left changes the odds of choosing left.
May combine two claims.
Findingreasoning§ ResultsPositive coefficients for trials further in the past than the last trial mean that choosing a particular alternative some time in the past increases the likelihood of choosing it again, independent of past reinforcers; alone these would produce a tendency to persist.
“Positive coefficients for the trials further in the past than the last trial mean that choosing a particular alternative some time in the past increases the likelihood of choosing it again, independent of the effects due to past reinforcers. Alone, these coefficients would produce a tendency to persist on an alternative.”
Quote in the paperSubstantial claim- The authors state this as an assumption: Past reinforcers and choices are linearly combined to determine choice on each trial.
- The authors state this as an assumption: The effects of past reinforcers and choices are symmetric: a past reinforcer or choice to the right changes the odds of choosing right by the same amount that a past reinforcer or choice to the left changes the odds of choosing left.
May combine two claims.
Findingown data§ DiscussionMonkeys adjusted their choice behavior in response to abrupt reversals in the prevailing reinforcer conditions, reaching an average steady-state of responding after obtaining relatively few reinforcers under the new schedule conditions.
“Monkeys adjusted their choice behavior in response to abrupt reversals in the prevailing reinforcer conditions, reaching an average steady-state of responding after obtaining relatively few reinforcers under the new schedule conditions.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ ResultsRunlengths for the nonpreferred alternative became very short, typically one trial, with a mean across all preferences of 1.05 trials and a standard deviation of 0.09.
“Almost as soon as one of the alternatives was preferred, the runlengths for the nonpreferred alternative became very short, typically one trial (mean across all preferences was 1.05 trials with a standard deviation of 0.09).”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown data§ ResultsFor both monkeys, the residual autocorrelations for the best-fitting model stayed mostly within the 95% confidence intervals expected from an independent random process, indicating that the residuals were largely unstructured.
“For both monkeys, the autocorrelations stayed mostly within these confidence intervals, indicating that the residuals were largely unstructured.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ ResultsThe best-fitting model's predictions captured the steady-state average as well as the dynamics of the transitions between blocks.
“The model predictions captured the steady-state average as well as the dynamics of the transitions between blocks.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ DiscussionBy accounting for the effects of past choices, the monkeys showed a short-term tendency to alternate as well as a longer-term tendency to persist on the more frequently chosen alternative.
“By accounting for the effects of past choices we showed that our monkeys have a short-term tendency to alternate as well as a longer-term tendency to persist on the more frequently chosen alternative.”
Quote in the paperSubstantial claim- The authors state this as an assumption: Past reinforcers and choices are linearly combined to determine choice on each trial.
- The authors state this as an assumption: The effects of past reinforcers and choices are symmetric: a past reinforcer or choice to the right changes the odds of choosing right by the same amount that a past reinforcer or choice to the left changes the odds of choosing left.
May combine two claims.
Findingown data§ ResultsThe pattern of results for reinforcer history is similar for both animals: the most recent reinforcers strongly increased the odds of choosing the reinforced alternative again, and this influence decayed as reinforcers receded in time.
“The pattern of results for reinforcer history is similar for both animals; the most recent reinforcers strongly increased the odds of choosing the reinforced alternative again, and this influence decayed as reinforcers receded in time.”
Quote in the paperSubstantial claim- The authors state this as an assumption: Past reinforcers and choices are linearly combined to determine choice on each trial.
- The authors state this as an assumption: The effects of past reinforcers and choices are symmetric: a past reinforcer or choice to the right changes the odds of choosing right by the same amount that a past reinforcer or choice to the left changes the odds of choosing left.
May combine two claims.
Findingown data§ ResultsThe actual runlength data systematically deviate from and reject the purely probabilistic model.
“The actual runlength data systematically deviate from and hence reject this model”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ ResultsThere was little or no spatial bias towards either alternative, consistent with the steady-state analysis using the generalized matching law.
“There was little or no spatial bias towards either alternative, which was consistent with our steady-state analysis using the generalized matching law.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingreasoning§ ResultsThe negative coefficient for the last trial means that choosing a particular alternative decreased the odds of choosing that alternative again on the next trial, independent of reinforcer history; alone this would produce a tendency to alternate.
“The negative coefficient for the last trial means that choosing a particular alternative decreased the odds of choosing that alternative again on the next trial, independent of any effects due to reinforcer history. Alone, this coefficient would produce a tendency to alternate.”
Quote in the paperSubstantial claim- The authors state this as an assumption: Past reinforcers and choices are linearly combined to determine choice on each trial.
- The authors state this as an assumption: The effects of past reinforcers and choices are symmetric: a past reinforcer or choice to the right changes the odds of choosing right by the same amount that a past reinforcer or choice to the left changes the odds of choosing left.
May combine two claims.
Findingown data§ ResultsThe monkeys tend to stay at the richer alternative, switching briefly to sample the leaner alternative.
“Instead, they show that the monkeys tend to stay at the richer alternative, switching briefly to sample the leaner alternative.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Study design and conductown data§ MethodThe data analyzed were 67,827 completed trials from Monkey H and 47,160 completed trials from Monkey B.
“The data analyzed were 67,827 completed trials from Monkey H and 47,160 completed trials from Monkey B.”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim.
Premisecitation§ AbstractThe strict matching law equates the relative number of choices to the relative reinforcer frequency.
“The strict matching law equates these two quantities; the relative number of choices matches the relative reinforcer frequency (Herrnstein, 1961).”
Quote in the paperSubstantial claim0 of 1 sources checked- cites Herrnstein, 1961 source
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Study design and conductown data§ MethodThe mean number of trials per block observed was 121 trials for Monkey H and 125 trials for Monkey B, after excluding aborted trials.
“The mean number of trials per block observed was 121 trials for Monkey H and 125 trials for Monkey B, after excluding aborted trials.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Premisecitation§ AbstractThe generalized matching law for reinforcer frequency and magnitude assumes that these attributes have independent effects but allows for differential levels of control by each variable.
“The generalized matching law for reinforcer frequency and magnitude assumes that these attributes have independent effects (Baum & Rachlin, 1969), but allows for differential levels of control by each variable;”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Baum & Rachlin, 1969
Not checked in the free run.
Classified as probably not a substantial claim.
Premisecitation§ AbstractSingle neurons in a number of cortical areas have activity correlated with reinforcer frequency and magnitude.
“Single neurons in a number of cortical areas have activity correlated with reinforcer frequency (Barraclough, Conroy, & Lee, 2004; Platt & Glimcher, 1999; Sugrue et al., 2004) and magnitude (Platt & Glimcher, 1999).”
Quote in the paperSubstantial claim0 of 3 sources checkedProbably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductnone given§ MethodAll the data reported were collected after at least 3 months of training on the choice task.
“All the data reported were collected after at least 3 months of training on the choice task.”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim.
Premisecitation§ ResultsIf monkeys chose purely probabilistically by flipping a weighted coin on each trial with weight dictated by degree of preference, runlengths would be distributed geometrically with mean equal to the reciprocal of the coin weight.
“If the monkeys chose in a purely probabilistic manner by flipping a weighted coin on each trial, with the weight dictated by the degree of preference (e.g., a 2∶1 preference gives a two-thirds probability of choosing the preferred alternative on each trial), the runlengths would be distributed geometrically with a mean equal to the reciprocal of the coin weight.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites Houston & Sumida, 1987
Not checked in the free run.
- The authors state this as an assumption: In the purely probabilistic baseline model, choices are independent between trials, so the degree of weighting of the coin fully specifies the runlength distributions.
May combine two claims.
Interpretationown data§ ResultsThe generalized matching law is a reasonable description of the monkeys' data, even though it is typically used to describe data after many sessions rather than trials of training under the same reinforcer conditions.
“This indicates that the generalized matching law is a reasonable description of our data, even though it typically is used to describe data after many sessions, rather than trials, of training under the same reinforcer conditions.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationown data§ AbstractBehavioral models incorporating dependence on both past reinforcers and choices may provide more accurate predictions, which will be essential for correlation with neural activity.
“The present results suggest that behavioral models incorporating dependence on both past reinforcers and choices may provide more accurate predictions, which will be essential for correlation with neural activity.”
Quote in the paperSubstantial claimMay combine two claims.
Premisecitation§ AbstractThe generalized matching law describes an enormous amount of data collected from many species and allows one to predict average choice behavior under different conditions.
“The generalized matching law describes an enormous amount of data collected from many species (de Villiers, 1977), and allows one to predict average choice behavior under different conditions, such as for arbitrary combinations of reinforcer frequency and magnitude.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites de Villiers, 1977
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Study design and conductown data§ MethodThe monkeys rarely aborted trials (7% for Monkey H and 6% for Monkey B), and these trials were excluded from analyses.
“The monkeys rarely aborted trials (7% and 6% of trials for Monkey H and Monkey B, respectively), and these trials were excluded from our analyses.”
Quote in the paperNot a substantial claimMay combine two claims.
Premisenone given§ ResultsThe generalized matching law only describes average choice and is silent regarding the sequences of choices underlying those averages.
“Although the generalized matching law fits the steady-state behavior that we measured, it only describes average choice. It is silent regarding the sequences of choices underlying these averages.”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
Premisecitation§ AbstractMany plausible theoretical models incorporate some form of reinforcer rate estimation using linear weightings of past reinforcers.
“Many of the more plausible—in the sense that animals may actually implement them—theoretical models incorporate some form of reinforcer rate estimation using linear weightings of past reinforcers (e.g., Killeen, 1981; Luce, 1959).”
Quote in the paperSubstantial claim0 of 2 sources checked- cites Killeen, 1981
Not checked in the free run.
- cites Luce, 1959
Not checked in the free run.
Classified as probably not a substantial claim. May combine two claims.
Premisecitation§ ResultsDifferences in AIC values represent the degree of evidence in favor of the best-fitting model, and values greater than 10 provide strong support for the model with the smallest AIC value.
“The differences in AIC values in Table 3 represent the degree of evidence in favor of the best-fitting model, and the simpler models were selected to give a sense of the contribution of each model component. The larger the difference the less plausible a model is compared to the best model; values greater than 10 on this scale provide strong support for the model with the smallest AIC value (Burnh”
Quote in the paperSubstantial claim0 of 1 sources checked- cites Burnham & Anderson, 1998 source
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Interpretationreasoning§ DiscussionThe decision process can be split into a first stage that estimates the subjective value of each alternative from past experience and a second stage that forms a decision by comparing these estimates.
“In the first stage, the subjective value of each alternative is estimated from past experience, and in the second stage a decision is formed by comparing these estimates.”
Quote in the paperNot a substantial claimMay combine two claims.
Interpretationown data§ ResultsA model that only incorporates reinforcer history, excluding choice history regressors, is inadequate and indicates the need to incorporate the effects of past choices to account for the response-by-response structure in the task.
“This model is inadequate, and clearly indicates the need to incorporate the effects of past choices to account for the response-by-response structure in our task.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Interpretationreasoning§ DiscussionBecause the model is linear in its parameters, the coefficients weighting past reinforcers can be rescaled so that they sum to 1.
“Because the model is linear in the parameters, the coefficients weighting past reinforcers can be rescaled so they sum to 1.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Interpretationreasoning§ DiscussionThe first stage of the model includes the effects of past reinforcers, which provide estimates of the rate of reinforcement.
“As we have sketched it, the first stage includes the effects of past reinforcers, which we think of as providing estimates of the rate of reinforcement.”
Quote in the paperNot a substantial claim- The authors state this as an assumption: Animals form internal representations about recently obtained reinforcers.
May combine two claims.
Interpretationreasoning§ ResultsThe fix-and-sample pattern comes about because larger or more frequent reinforcers increase the likelihood of repeating choices to the alternative that yields them; momentary decreases in rich reinforcers eventually cause a switch to the lean alternative, followed by a tendency to switch immediately back to the rich alternative due to longer-term choice history effects.
“This pattern comes about because larger or more frequent reinforcers increase the likelihood of repeating choices to the alternative that yields them. Momentary decreases in rich reinforcers eventually cause a switch to the lean alternative, followed by a tendency to switch immediately back to the rich alternative due to longer-term choice history effects.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Interpretationreasoning§ DiscussionThe estimate of the difference in average reinforcer rate has units of reinforcer magnitude per trial and is passed to the second stage to form a choice probability.
“This estimate has units of reinforcer magnitude per trial, and is passed to the second stage to form a choice probability.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Premisecitation§ ResultsBaum, Schwendiman, and Bell (1999) observed the fix-and-sample pattern in pigeons under concurrent VI VI schedules.
“Baum, Schwendiman, and Bell (1999) observed this pattern of behavior in pigeons under concurrent VI VI schedules, terming it “fix-and-sample.””
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Baum, Schwendiman, and Bell (1999)
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing).
Interpretationreasoning§ DiscussionThe stronger undermatching observed may have occurred because the reinforcement contingencies were reversed many times during a single session.
“In addition, we may have observed stronger undermatching because we reversed the reinforcement contingencies many times during a single session.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Premisecitation§ DiscussionBaum et al. showed that the sequential structure varied depending on presence or absence of a changeover delay; pigeons adjust their patterns of choice behavior to respect fluctuations in local probability of reinforcement.
“Moreover, Baum et al. showed that the sequential structure varied depending on presence or absence of a changeover delay; pigeons adjust their patterns of choice behavior to respect the fluctuations in local probability of reinforcement.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Baum et al.
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing).
Premisecitation§ DiscussionMany theoretical models of foraging and repeated choice assume that the rate of prey encounter or reinforcement is a fundamental variable that animals use to achieve the computational goals of maximizing fitness or reinforcement.
“Many theoretical models of foraging and repeated choice behavior assume that the rate of prey encounter or reinforcement is a fundamental variable that animals use to achieve the computational goals of maximizing fitness or reinforcement (Stephens & Krebs, 1986).”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Stephens & Krebs, 1986
Not checked in the free run.
May combine two claims.
Interpretationreasoning§ ResultsResponse-by-response dependencies could have arisen from effects of past reinforcers and/or past choices, but sequential statistics like runlengths cannot reveal how this occurs because they do not take into account when reinforcers were delivered.
“These response-by-response dependencies could have arisen from the effects of past reinforcers and/or past choices, but how this occurs cannot be revealed through sequential statistics like runlengths because they do not take into account when reinforcers were delivered.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Premisecitation§ DiscussionIt is common to split the decision process into valuation and comparison stages.
“It is common to split the decision process in this manner (e.g., Davis, Staddon, Machado, & Palmer, 1993; Houston, Kacelnik, & McNamara, 1982; Luce, 1959).”
Quote in the paperNot a substantial claim0 of 3 sources checked- cites Davis, Staddon, Machado, & Palmer, 1993
Not checked in the free run.
- cites Houston, Kacelnik, & McNamara, 1982
Not checked in the free run.
- cites Luce, 1959
Not checked in the free run.
May combine two claims.
Interpretationown data§ ResultsRelative to Monkey H, the coefficients for Monkey B are initially larger but decay more quickly, indicating that recent reinforcers would shift preference more strongly but their effects are more local in time.
“Relative to Monkey H, the coefficients for Monkey B are initially larger, but also decay more quickly, indicating that recent reinforcers would shift preference more strongly, but that their effects are more local in time.”
Quote in the paperNot a substantial claim- The authors state this as an assumption: Past reinforcers and choices are linearly combined to determine choice on each trial.
- The authors state this as an assumption: The effects of past reinforcers and choices are symmetric: a past reinforcer or choice to the right changes the odds of choosing right by the same amount that a past reinforcer or choice to the left changes the odds of choosing left.
Probably not a substantial claim: may not pass S3 (load-bearing).
Premisecitation§ DiscussionRate estimation is usually implemented by a weighted average with exponential decay.
“Rate estimation is usually implemented by a weighted average with exponential decay (Killeen, 1981, 1994), which captures the intuitive notion that because natural environments are nonstationary, recent events should weigh more heavily in memory than long-past events (Cowie, 1977).”
Quote in the paperNot a substantial claim0 of 2 sources checked- cites Killeen, 1981, 1994
Not checked in the free run.
- cites Cowie, 1977 source
Not checked in the free run.
May combine two claims.
Premisecitation§ DiscussionHouston and McNamara (1981) prove that reinforcer rate is maximized by repeating a deterministic sequence; an optimal subject would choose the rich alternative a fixed number of times followed by a single choice of the lean alternative.
“Houston and McNamara (1981) prove that reinforcer rate is maximized by repeating a deterministic sequence; an optimal subject would choose the rich alternative a fixed number of times (dictated by the particular schedules) followed by a single choice of the lean alternative (see also Staddon et al., 1981).”
Quote in the paperSubstantial claim0 of 2 sources checked- cites Houston and McNamara (1981)
Not checked in the free run.
- cites Staddon et al., 1981 source
Not checked in the free run.
May combine two claims.
Interpretationreasoning§ DiscussionIn such tasks, it eventually pays to choose the lean alternative, but it is never worth staying more than one trial.
“Because the probability of reinforcement grows geometrically with time or responses spent away from the lean alternative in tasks like the one we used, it eventually pays to choose that alternative, but because its probability is reset to its initial low value once chosen it is never worth staying more than one trial.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Premisecitation§ DiscussionDopaminergic neurons in the substantia nigra pars compacta and the ventral tegmental area appear to be important for estimating reinforcement rate.
“For example, the dopaminergic neurons in the substantia nigra pars compacta (SNC) and the ventral tegmental area (VTA) appear to be important for estimating reinforcement rate.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S2 (checkable).
Interpretationreasoning§ DiscussionCharacterizing the effects of past reinforcers and choices allows a finer separation of these effects at the neural level.
“characterizing the effects of past reinforcers and choices allows a finer separation of these effects at the neural level.”
Quote in the paperNot a substantial claimMay combine two claims.
Premisecitation§ DiscussionBayer and Glimcher showed that the number of action potentials discharged by individual SNC neurons is proportional to the magnitude of the difference between the expected and obtained reinforcer, supporting the hypothesis that dopamine neurons underlie computation of prediction error.
“They showed that the number of action potentials discharged by individual SNC neurons is proportional to the magnitude of the difference between the reinforcer expected (vi−1) and the reinforcer actually obtained (ri), thereby lending strong support to the hypothesis that dopamine neurons underlie the computation of prediction error.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites Bayer and Glimcher (2005) source
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing).
Premisecitation§ DiscussionEvidence indicates that frontal cortex and the basal ganglia are important for the expression and learning of motor sequences.
“This idea is consistent with evidence that frontal cortex and the basal ganglia—which are densely interconnected—are important for the expression and learning of motor sequences (Hikosaka et al., 1999; Tanji, 2001; Tanji & Hoshi, 2001).”
Quote in the paperNot a substantial claim0 of 3 sources checked- cites Hikosaka et al., 1999 source
Not checked in the free run.
- cites Tanji, 2001
Not checked in the free run.
- cites Tanji & Hoshi, 2001
Not checked in the free run.
May combine two claims.
Premisecitation§ DiscussionThese neurons send dense projections to prefrontal cortex and striatum, and current evidence suggests these areas may use a prediction error to estimate reinforcer rate.
“These neurons send dense projections to the prefrontal cortex and the striatum, and current evidence suggests that these areas may use a prediction error to estimate reinforcer rate (Barraclough et al., 2004; Haruno et al., 2004; O'Doherty et al., 2004).”
Quote in the paperNot a substantial claim0 of 3 sources checkedProbably not a substantial claim: may not pass S3 (load-bearing).
Premisecitation§ DiscussionExperiments with monkeys and humans have shown that SNC/VTA neurons encode a prediction error, the difference between the reinforcer expected and the reinforcer obtained within a trial.
“Experiments with monkeys and humans have shown that these neurons encode a prediction error, the difference between the reinforcer expected and the reinforcer obtained within a trial (O'Doherty et al., 2004; Schultz, 1998).”
Quote in the paperNot a substantial claim0 of 2 sources checkedMay combine two claims.
Premisereasoning§ DiscussionAppropriate use of recent memory for past responses can generate tendencies to shift away from or persist on recently chosen alternatives, and is necessary for producing patterned sequences of responses.
“Appropriate use of recent memory for past responses can generate tendencies to shift away from, or to persist on, recently chosen alternatives (negative recency and positive recency), and is necessary for producing patterned sequences of responses.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing), S4 (based).
Interpretationnone given§ DiscussionThe covariation of neural activity in parietal cortex with behaviorally relevant variables likely reflects computations carried out in other brain areas.
“The covariation of neural activity in the parietal cortex with behaviorally relevant variables likely reflects computations carried out in other brain areas.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Premisecitation§ DiscussionBayer and Glimcher (2005) linked SNC activity to reinforcement-rate estimation using the exponentially weighted average.
“Bayer and Glimcher (2005) linked SNC activity to reinforcement-rate estimation using the exponentially weighted average described above.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Bayer and Glimcher (2005) source
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing).
Premisecitation§ DiscussionDevenport and Devenport (1994) propose a temporal weighting rule that weights past reinforcers hyperbolically with respect to units of time.
“For example, Devenport and Devenport (1994) propose a temporal weighting rule that weights past reinforcers hyperbolically (with respect to units of time).”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Devenport and Devenport (1994)
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Premisecitation§ DiscussionThe decision stage of many choice models uses rules including selecting the most valuable alternative, matching choice proportions to local rates of reinforcement, and the logistic/softmax/logit function.
“The decision stage of many choice models uses rules including simply selecting the most valuable alternative (Herrnstein & Vaughan, 1980), matching choice proportions to the local rates of reinforcement (Kacelnik, Krebs, & Ens, 1987), and the logistic function we have used, which is commonly referred to as the softmax (Sutton & Barto, 1998) or logit (Camerer & Ho, 1998) decision rule.”
Quote in the paperNot a substantial claim0 of 3 sources checked- cites Herrnstein & Vaughan, 1980
Not checked in the free run.
- cites Kacelnik, Krebs, & Ens, 1987
Not checked in the free run.
- cites Sutton & Barto, 1998
Not checked in the free run.
Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing). May combine two claims.
Premisecitation§ DiscussionOne can only remember so much information, but what one does with that memory presumably depends on reinforcement contingencies and other factors.
“This captures the idea that one can only remember so much information, but it is distinct from what one does with that memory, which presumably depends on reinforcement contingencies and other factors (Glimcher, 2005; Neuringer, 2002).”
Quote in the paperNot a substantial claim0 of 2 sources checkedProbably not a substantial claim: may not pass S3 (load-bearing), S4 (based).
Premisereasoning§ DiscussionThese variables must be represented in the nervous system if they are to affect choice.
“These variables must be represented in the nervous system if they are to affect choice”
Quote in the paperNot a substantial claimMay combine two claims.
Premisenone given§ DiscussionIn tasks like the one used, the probability of reinforcement grows geometrically with time or responses spent away from the lean alternative, and is reset to its initial low value once chosen.
“Because the probability of reinforcement grows geometrically with time or responses spent away from the lean alternative in tasks like the one we used, it eventually pays to choose that alternative, but because its probability is reset to its initial low value once chosen it is never worth staying more than one trial.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).
Premisenone given§ DiscussionFor an animal foraging for food, evaluating which patch to forage at is a complex combination of estimating the reinforcement rate at each patch, the likelihood that an alternative patch has recently become richer, the risk of predation, and other factors.
“For an animal foraging for food, evaluating which patch to forage at is a complex combination of estimating the reinforcement rate at each patch, the likelihood that an alternative patch has recently become richer, the risk of predation, and so on.”
Quote in the paperNot a substantial claim
The paper relies on this without support.
Monkeys are commonly used as subjects in neuroscientific research but are rarely used as subjects in matching experiments.
“However, monkeys are commonly used as subjects in neuroscientific research, but they are rarely used as subjects in matching experiments, and the behavioral research that has been done with monkeys (Anderson, Velkey, & Woolverton, 2002; Iglauer & Woods, 1974) differs in a number of procedural details from the behavioral methods used in neuroscience.”
The authors state this as an assumption.
Past reinforcers and choices are linearly combined to determine choice on each trial.
“We assume that past reinforcers and choices are linearly combined to determine choice on each trial, which allows us to write the logistic regression,”
The authors state this as an assumption.
The effects of past reinforcers and choices are symmetric: a past reinforcer or choice to the right changes the odds of choosing right by the same amount that a past reinforcer or choice to the left changes the odds of choosing left.
“We simplify the model by assuming that the effects of past reinforcers and choices are symmetric; a past reinforcer or a choice to the right alternative changes the odds of choosing right by the same amount that a past reinforcer or a choice to the left alternative changes the odds of choosing left.”
The authors state this as an assumption.
In the purely probabilistic baseline model, choices are independent between trials, so the degree of weighting of the coin fully specifies the runlength distributions.
“This is a useful baseline model because the assumption of independence between trials that defines this model means that the degree of weighting of the coin fully specifies the runlength distributions (e.g., Houston & Sumida, 1987).”
The authors state this as an assumption.
Animals form internal representations about recently obtained reinforcers.
“The terms Σ α(rR − rL) encapsulate our assumptions about the internal representations animals form about recently obtained reinforcers.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
A few studies have estimated the time constant of the reward filter from behavior, and assessed how past rewards affect choice selection.
“So far a few studies have estimated the time constant of this filter from behavior, and assessed how past rewards affect choice selection8-12”
From A reservoir of time constants for memory traces in cortical neurons (2011) · cites this paper as [8]
The decision behavior is influenced by past rewards harvested locally in time, in agreement with the observed monkey's behavior.
“Hence, the decision behavior is influenced by past rewards harvested locally in time, in agreement with the observed monkey’s behavior (Sugrue et al., 2004; Lau and Glimcher, 2005).”
From Decision Making in Recurrent Neuronal Circuits (2008) · cites this paper as Lau and Glimcher, 2005
In reinforcement models for reward-dependent choice, the DV is defined by values of response options which are deterministically updated according to past rewards, whereas the choice is generated by a probabilistic decision rule (e.g., a softmax criterion) based on the DV.
“On the other hand, in reinforcement models for reward-dependent choice (Barraclough et al., 2004; Sugrue et al., 2004, 2005; Lau and Glimcher, 2005), the DV is defined by values of response options which are deterministically updated according to past rewards, whereas the choice is generated by a probabilistic decision rule (e.g., a softmax criterion) based on the DV.”
From Decision Making in Recurrent Neuronal Circuits (2008) · cites this paper as Lau and Glimcher, 2005
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Reinforcement Learning: An Introduction
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- Authors
- Lau, B., & Glimcher, P. W.
- Affiliations
- New York University (US)
- Corresponding author
- Lau, Brian
- Venue
- Journal of the Experimental Analysis of Behavior
- Publisher
- Wiley
- Published
- 2005-11
- Volume
- 84
- Issue
- 3
- Pages
- 555-579
- ISSN
- 0022-5002 (ISSN-L)
- PMC
- PMC1389781
- OpenAlex
- W2001643038
- Cited by
- 485
- References
- 106
- Citations by year
- 2026: 13 · 2025: 15 · 2024: 18 · 2023: 18 · 2022: 17 · 2021: 26 · 2020: 50 · 2019: 29 · 2018: 24 · 2017: 26 · 2016: 24 · 2015: 24 · 2014: 32 · 2013: 24 · 2012: 20
- FWCI
- 10.43
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Licence
- Locations
- Journal of the Experimental Analysis of Behavior (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Funders
- York University
- National Defense Science and Engineering Graduate
- National Eye Institute (EY010536, R01EY010536)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural and Behavioral Psychology Studies
- Social Sciences › Decision Sciences › General Decision Sciences › Decision-Making and Behavioral Economics
- Social Sciences › Psychology › Developmental and Educational Psychology › Behavioral and Psychological Studies
- Keywords
- matching law, generalized matching law, choice behavior, reinforcement learning, reinforcement magnitude, response ratio, steady-state behavior, rhesus monkeys
- MeSH terms
- Animals, Attention, Choice Behavior, Color Perception, Conditioning, Operant, Discrimination Learning, Electrooculography, Eye Movements, Fixation, Ocular, Macaca mulatta, Male, Motivation, Probability Learning, Reinforcement Schedule, Retention, Psychology, Signal Processing, Computer-Assisted, Visual Fields
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-10.
Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-10.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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