The effect of logarithmic transformation on estimating the parameters of the generalized matching law

The generalized matching law was initially stated as a nonlinear relation between reinforcement-rate ratios and response-rate ratios. Often, the variables of the law are transformed logarithmically to remove the nonlinearity; empirical results are then fit to the model through least-squares regression. However, the logarithmic expression of the matching law is a biased statistical representation of the law itself. In particular, the logarithmic transformation alters the quantitative conclusions to be drawn from a least-squares regression analysis. A Monte Carlo study of the effect of transforming matching-law data demonstrated that (a) the estimates of one or both of the parameters of the generalized matching law are biased, (b) the measure of goodness of fit (R(2)) is inaccurate, and (c) predictions generated by the fitted parameters are incorrect. Alternative approaches to logarithmic transformations are shown to alleviate these problems.