Comparing the fits of the different enzyme inhibition models requires thinking both about enzyme mechanism and about statistics. Some notes:
•The mixed model generalizes competitive, noncompetitive and uncompetitive. Each of those three models are special cases of the mixed-model.
•Comparing R2 is an easy way to compare fits, but not a very good method.
•The extra sum-of-squares F test is only valid when one model is a special case of (is nested within) the other model. The mixed model is a general equation that includes competitive, uncompetitive and noncompetitive inhibition as special cases, so it is OK to compare the mixed model with any of the other three by F test. The competitive model is a special case of the uncompetitive or noncompetitive modes, so you can compare the competitive model with either uncompetitive or noncompetitive models by F test. The uncompetitive and noncompetitive models are not nested so cannot be compared by F test.