On applying the matching law to between-subject data

Caron, Pier-Olivier

doi:10.1016/j.anbehav.2013.01.022

Cited by 9 publications

(10 citation statements)

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“…Matching behavior is a single subject‐orientated model; that is, parameters of the GML are unique to a given subject (Caron, ). These parameters can be different from one subject to the other.…”

Section: Challenges That Arise When Pooling Individual Modelsmentioning

confidence: 99%

“…One strategy to support a general claim using a within‐subject design is to pool subjects. However, pooling has led to troublesome conclusions, since the use of direct aggregation of data across subjects or averaged parameters could not take into account both within‐ and between‐subjects variances (Caron, ). Depending on the case, researchers often (a) pooled data across ratios so that each ratio was analyzed independently; (b) pooled ratios across subjects, reducing the between‐subjects variances and eliminating the variance induced by the ratios; (c) averaged subjects' behaviors in a single mean for each ratio, thus eliminating the within‐subject variances and potentially overemphasizing unusual matching behavior (Caron, ).…”

Section: Challenges That Arise When Pooling Individual Modelsmentioning

confidence: 99%

“…However, pooling has led to troublesome conclusions, since the use of direct aggregation of data across subjects or averaged parameters could not take into account both within‐ and between‐subjects variances (Caron, ). Depending on the case, researchers often (a) pooled data across ratios so that each ratio was analyzed independently; (b) pooled ratios across subjects, reducing the between‐subjects variances and eliminating the variance induced by the ratios; (c) averaged subjects' behaviors in a single mean for each ratio, thus eliminating the within‐subject variances and potentially overemphasizing unusual matching behavior (Caron, ). Inappropriately pooling data can conceal the number of different ratios used, the number of data points by ratio, and the variability (and consistency) between individuals, all of which are critical pieces of information about the precision of the slope (sensitivity) and the intercept (bias) that, when lost, severely limit the results' generalization.…”

Section: Challenges That Arise When Pooling Individual Modelsmentioning

confidence: 99%

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Multilevel analysis of matching behavior

Caron

2019

J Exper Analysis Behavior

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Multilevel modeling has been considered a promising statistical tool in the field of the experimental analysis of behavior and may serve as a convenient statistical analysis for matching behavior because it structures data in groups (or levels) to account simultaneously for the within‐subject and between‐subject variances. Heretofore, researchers have sometimes pooled data erroneously from different subjects in a single analysis by using average ratios, average response and reinforcer rates, aggregation of subjects, etc. Unfortunately, this leads to loss of information and biased estimations, which can severely undermine generalization of the results. Instead, a multilevel approach is advocated to combine several subjects' matching behavior. A reanalysis of previous data on matching behavior is provided to illustrate the method and point out its advantages. It illustrates that multilevel regression leads to better estimations, is more convenient, and offers more behavioral information. We hope this paper will encourage the use of multilevel modeling in the statistical practices of behavior analysts.

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Section: Challenges That Arise When Pooling Individual Modelsmentioning

confidence: 99%

Section: Challenges That Arise When Pooling Individual Modelsmentioning

confidence: 99%

Section: Challenges That Arise When Pooling Individual Modelsmentioning

confidence: 99%

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Multilevel analysis of matching behavior

Caron

2019

J Exper Analysis Behavior

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“… 3. Remember that the GML is a within-subject model (Caron, 2013) and that the sample size is the number of sessions by subject. …”

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Matching without learning

Caron

2015

Adaptive Behavior

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Matching behavior is a phenomenon describing response rate ratios of an organism as a function of their associated reinforcer rate ratios. The generalized matching law (GML), its quantitative formulation, has been frequently found to explain over 80% of the variance in concurrent reinforcement schedules. However, a previous paper found by means of Monte Carlo simulations that matching behavior could be due to environmental constraints on behavior rather than a mere decision-making process. The purpose of the current study is to systemically investigate the influence of constraints induced by concurrent schedules of reinforcement. A Monte Carlo simulation was carried out. Results showed that the GML reached much better explained variances with real (and artificial) organisms than the current simulated results. Thus, a learning process seems partly necessary to generate matching behavior. According to the current findings, concurrent reinforcement schedules clearly induced a quantitative dependency between behavior rates and reinforcer rates. The simulation demonstrates that matching behavior is not only a consequence of a behavioral (decision-making) process, but of environmental conditions also.

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“…Even if I agree with most points raised by McDowell, there are 2 important issues within his reanalysis. Two out of 6 studies relied on pooled-subject data that are inappropriate for an investigation of the matching law (Caron, 2013). Moreover, the combined equation was not systemically investigated through all data sets.…”

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On the empirical status of the matching law: Comment on McDowell (2013).

Caron¹

2013

Psychological Bulletin

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The matching law, regardless of the version, is a mathematical model that accounts for an organism's response rate as a function of the reinforcer rate. McDowell (2013) investigated to which extent a combined version of the quantitative law of effect (Herrnstein, 1970) and the generalized matching law (Baum, 1974) accounts for a substantial amount of the variance through several data sets. Even if I agree with most points raised by McDowell, there are 2 important issues within his reanalysis. Two out of 6 studies relied on pooled-subject data that are inappropriate for an investigation of the matching law (Caron, 2013). Moreover, the combined equation was not systemically investigated through all data sets. The current study casts some doubt on the empirical status of modern matching equations and thus shows that they still deserve extensive attention.Keywords: choice, matching law, pooled data, within-subject varianceThe matching law is a quantitative model that describes the response allocation of an organism according to the relative reinforcer ratio (Herrnstein, 1961). The model has evolved into two equations: the quantitative law of effect proposed by Herrnstein (1970) and the generalized matching law proposed by Baum (1974). The quantitative law of effect conceptualizes the absolute response rate as a hyperbolic function of the absolute reinforcer rate, respectively, Bs and rs in Equation 1:Theoretically, the parameter k corresponds to absolute response rate, and r e corresponds to extraneous reinforcers. Herrnstein's (1970) conceptualization implies that the absolute quantity of behavior and extraneous reinforcers are constant within an experimental condition. Thus, the quantitative law of effect is more a theory than a purely descriptive equation such as the generalized matching law,where Bs and rs are the same as Equation 1. The generalized matching law conceptualizes response ratios and reinforcer ratios as a power function. The exponent a is referred to as sensitivity, and the coefficient b is referred to as bias. The power function is also known in its logarithmic form:Every parameter, a, b, r e , k, and the explained variance from each equation, are obtained via an ordinary least-squares regression where parameters are generally free to vary, even though fewer studies imposed constraints on the parameters. McDowell (2013) attempted to unify both equations into a single framework. He evaluated through extensive data sets to which extent the modern matching equations (Equations 6 -9 from the target article) can account for a substantial quantity of the variance and whether residuals appeared systematically correlated. However, McDowell did not systematically investigate Equation 6= from target article and numbered alike here. Moreover, McDowell used two conceptually inappropriate data sets out of six sets. Instead of analyzing the matching law from single-subject data, he conducted analyses on pooled-subject data. Therefore, his analyses violate a simple assumption of matching theory, that is, the mat...

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On applying the matching law to between-subject data

Abstract: International audienceSome researchers misunderstand that the matching law accounts for individual choice. In fact, some researchers have conducted inappropriate statistical analyses on between-subject data. The current article shows how misleading between-subject analyses may be

Cited by 9 publications

References 17 publications

Multilevel analysis of matching behavior

Multilevel analysis of matching behavior

Matching without learning

On the empirical status of the matching law: Comment on McDowell (2013).

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