One assumption of the matching approach to choice is that different independent variables control choice independently of each other. We tested this assumption for reinforcer rate and magnitude in an extensive parametric experiment. Five pigeons responded for food reinforcement on switching-key concurrent variable-interval variable-interval schedules. Across conditions, the ratios of reinforcer rates and of reinforcer magnitudes on the two alternatives were both manipulated. Control by each independent variable, as measured by generalized-matching sensitivity, changed significantly with the ratio of the other independent variable. Analyses taking the model-comparison approach, which weighs improvement in goodness-of-fit against increasing number of free parameters, were inconclusive. These analyses compared a model assuming constant sensitivity to magnitude across all reinforcer-rate ratios with two alternative models. One of those alternatives allowed sensitivity to magnitude to vary freely across reinforcer-rate ratios, and was less efficient than the common-sensitivity model for all pigeons, according to the Schwarz-Bayes information criterion. The second alternative model constrained sensitivity to magnitude to be equal for pairs of reinforcer-rate ratios that deviated from unity by proportionately equal amounts but in opposite directions. This model was more efficient than the common-magnitude-sensitivity model for 2 of the pigeons, but not for the other 3. An analysis of variance, carried out independently of the generalized-matching analysis, also showed a significant interaction between the effects of reinforcer rate and reinforcer magnitude on choice. On balance, these results suggest that the assumption of independence inherent in the matching approach cannot be maintained. Relative reinforcer rates and magnitudes do not control choice independently. (Contains 2 tables, 5 figures and 1 footnote.)