Our proposed re-parameterized regression approach rests on critical assumptions and has some potential weaknesses that accompany its clear strengths. The assumptions are not unique to the new methods we proposed here, but apply equally to use of standard approaches used to estimate the cross-over point in interactions. Moreover, assumptions should always be evaluated to the extent possible. Threats to the validity of conclusions using any statistical procedures, our re-parameterized models included, should always be investigated, and conclusions should be qualified if assumptions are not fully met. In our opinion, the benefits of our re-parameterized equations outweigh any potential drawbacks to their use and supplement in informative ways traditional approaches to testing interactions using regression methods.
