One possible weakness of re-parameterized models is the empirical identification of parameters for interactions with nil or small effect sizes. In the limit, if the interaction were completely absent, iterative fitting of model estimates would not converge and the estimate of the cross-over point Ĉ would be empirically unidentified and inestimable; if the interaction coefficient were a very small positive or negative value, the cross-over point Ĉ would be difficult to estimate and might tend to ±∞ with extremely large SE. Although some might view lack of convergence as a problem, it might be seen as a strength of the procedure, indicating that the interaction effect may be small or non-existent. Or, if a test of an interaction were significant using a standard model, lack of convergence of a re-parameterized model may not be due to an extremely small interaction effect (e.g., one or more outliers may lead to non-convergence), and the researcher should explore the data more fully to isolate the problem.
