Abstract

CARON, Pier-Olivier. The generalized matching law: a Monte Carlo simulation. Acta comport. [online]. 2014, vol.22, n.2, pp. 169-179. ISSN 0188-8145.

The generalized matching law (GML) is a descriptive mathematical model that conceptualizes an organism's response ratios as a function of associated reinforcer ratios (Baum 1974). The matching equation has been used in several experimental and natural studies and results frequently showed explained variances (r2) over 80% and sensitivity of 0.80 (Davison & McCarthy 2010). This high level of r2 might suggest that constraints within operant conditioning procedures may inflate GML parameters. For instance, in most operant procedures, such as a concurrent variable-interval schedule of reinforcement, the amount of reinforcers obtained is always lower or equal to the amount of responses, which can be seen as an emergent property of feedback functions. The purpose of the current study is to apply the GML to pseudorandomly sampled data in which this constraint has been computed. A Monte Carlo simulation shows that the generalized matching law explained on average 47 % of the variance, with sensitivity around a value of 0.60 and bias of log c = 0.00. Results found in the current study could be used as an alternative null hypothesis for future studies in natural settings. For instance, explained variances of 0.62, 0.80, and 0.97 could be qualify, respectively, as small, medium and large differences compared to 0.47. The current study is finally compared to McDowell's (2004) simulations. McDowell computed behavioral processes, such as the selection by consequences (Skinner, 1981), within the organism whereas the current study investigates environmental and observational constraints on the regressions estimates. Current results suggest further investigations of underlying environmental constraints when studying the GML. Futures studies are necessary to assess what to expect from the GML when such constraints occur in the operant conditioning procedure.

Keywords : explained variance; matching law; Monte Carlo; simulation; feedback function.

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