Response Surface Optimization in Growth Curves Through Multivariate Analysis

A methodology is proposed to jointly model treatments with quantitative levels measured throughout time by combining the response surface and growth curve techniques. The model parameters, which measure the effect throughout time of the factors related to the second-order response surface model, are estimated. These estimates are made through a suitable transformation that allows to express the model as a classic MANOVA model, so the traditional hypotheses are formulated and tested. In addition, the optimality conditions throughout time are established as a set of specific combination factors by the fitted model. As a final step, two applications are analyzed using our proposed model: the first was previously analyzed with growth curves in another paper, and the second involves two factors that are optimized over time.