Comparing the generalized matching law and contingency discriminability model as accounts of concurrent schedule performance using residual meta-analysis

To compare the generalized matching law (Baum, W.M., 1974b. On two types of deviation from the matching law: bias and undermatching. J. Exp. Anal. Behav. 22, 231–242) and contingency discriminability model (Davison, M., Jenkins, P.E., 1985. Stimulus discriminability, contingency discriminability, and schedule performance. Anim. Learn. Behav. 13, 77–84) as accounts of concurrent schedule performance, we conducted a residual meta-analysis of response- and time-allocation data from 20 studies (n's = 886 and 774, respectively). Both models were fitted to the individual-subject data from each study, and residuals were obtained. Polynomial regressions were then performed on the pooled residuals to determine whether systematic trends were present as a function of predicted values. For the contingency discriminability model, the cubic coefficients were positive and statistically significant for both response- and time-allocation data. By contrast, no statistically significant systematic trend was obtained in the residuals for the generalized matching law. These results suggest that the relationship between log response allocation and log reinforcer allocation does not deviate significantly from linearity over an approximate range of +1.25 to −1.25 log units, consistent with the generalized matching law. Although qualitative criteria are also important in comparing models of behavioral phenomena, residual meta-analysis provides a powerful quantitative methodology for model selection and should prove useful in future research.