Cited by 490Neural and Behavioral Psychology StudiesDecision-Making and Behavioral EconomicsBehavioral and Psychological Studies

DYNAMIC RESPONSE-BY-RESPONSE MODELS OF MATCHING BEHAVIOR IN RHESUS MONKEYS

Open access
Lau, Brian, Glimcher, Paul W.·2005·Journal of the Experimental Analysis of Behavior

Abstract

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.

AI snapshot

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.

Integrity signals

Registry

Crossref · 10.1901/jeab.2005.110-04

Cites

97 of 97 references verified0 citation errors · 0 not checkable

Statistics

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Claims the paper makes

0 of 64 cited sources checked · 0 supported · 0 flagged

  • 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
  • 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
    § Results

    Adding 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 claim
  • May combine two claims.

    Findingown data
    § Abstract

    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.

    “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 claim
  • May combine two claims. The quote only partly states this claim.

    Findingown data
    § Results

    There 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 claim
  • May combine two claims.

    Findingown data
    § Results

    For 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
    § Results

    Positive 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
    § Discussion

    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.

    “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 claim
  • May combine two claims.

    Findingown data
    § Results

    Runlengths 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 claim
  • May combine two claims.

    Findingown data
    § Results

    For 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 claim
  • May combine two claims.

    Findingown data
    § Results

    The 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 claim
  • May combine two claims.

    Findingown data
    § Discussion

    By 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
    § Results

    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.

    “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
    § Results

    The 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 claim
  • May combine two claims.

    Findingown data
    § Results

    There 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 claim
  • May combine two claims.

    Findingreasoning
    § Results

    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 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
    § Results

    The 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 claim
  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Study design and conductown data
    § Method

    The 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 claim
  • Classified as probably not a substantial claim.

    Premisecitation
    § Abstract

    The 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
    § Method

    The 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 claim
  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation
    § Abstract

    The 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
    § Abstract

    Single 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 checked
    • cites Barraclough, Conroy, & Lee, 2004 source

      Not checked in the free run.

    • cites Platt & Glimcher, 1999 source

      Not checked in the free run.

    • cites Sugrue et al., 2004 source

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  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductnone given
    § Method

    All 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 claim
  • Classified as probably not a substantial claim.

    Premisecitation
    § Results

    If 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
    § Results

    The 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 claim
  • May combine two claims.

    Interpretationown data
    § Abstract

    Behavioral 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 claim
  • May combine two claims.

    Premisecitation
    § Abstract

    The 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
    § Method

    The 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 claim
  • May combine two claims.

    Premisenone given
    § Results

    The 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 claim
  • Classified as probably not a substantial claim.

    Premisecitation
    § Abstract

    Many 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
    § Results

    Differences 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
    § Discussion

    The 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 claim
  • May combine two claims.

    Interpretationown data
    § Results

    A 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 claim
  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationreasoning
    § Discussion

    Because 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 claim
  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationreasoning
    § Discussion

    The 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
    § Results

    The 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 claim
  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Interpretationreasoning
    § Discussion

    The 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 claim
  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Results

    Baum, 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
    § Discussion

    The 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 claim
  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation
    § Discussion

    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 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
    § Discussion

    Many 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
    § Results

    Response-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 claim
  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Discussion

    It 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
    § Results

    Relative 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
    § Discussion

    Rate 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
    § Discussion

    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 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
    § Discussion

    In 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 claim
  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Discussion

    Dopaminergic 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 claim
  • Probably not a substantial claim: may not pass S2 (checkable).

    Interpretationreasoning
    § Discussion

    Characterizing 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 claim
  • May combine two claims.

    Premisecitation
    § Discussion

    Bayer 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
    § Discussion

    Evidence 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
    § Discussion

    These 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 checked
    • cites Barraclough et al., 2004 source

      Not checked in the free run.

    • cites Haruno et al., 2004 source

      Not checked in the free run.

    • cites O'Doherty et al., 2004 source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Discussion

    Experiments 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 checked
    • cites O'Doherty et al., 2004 source

      Not checked in the free run.

    • cites Schultz, 1998 source

      Not checked in the free run.

  • May combine two claims.

    Premisereasoning
    § Discussion

    Appropriate 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 claim
  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationnone given
    § Discussion

    The 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 claim
  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Discussion

    Bayer 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
    § Discussion

    Devenport 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
    § Discussion

    The 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
    § Discussion

    One 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 checked
    • cites Glimcher, 2005 source

      Not checked in the free run.

    • cites Neuringer, 2002 source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Premisereasoning
    § Discussion

    These 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 claim
  • May combine two claims.

    Premisenone given
    § Discussion

    In 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 claim
  • Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

    Premisenone given
    § Discussion

    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 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
60 of 60
  • 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.”
5 of 5

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”
  • 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

Cites

Flagged first, then by citations

9 of the 106 references couldn’t be matched to a known paper.

Research works printed but not linked: 4

  1. Houston, 1982, Functional ontogeny, 140
  2. Kacelnik, 1987, Quantitative analyses of behaviour, Vol. 6: Foraging, 63
  3. Stephens, 1986, Foraging theory
  4. Williams, 1988, Stevens's handbook of experimental psychology, 167

Cited by

Sorted by citations

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)
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
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

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Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-10.

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