Response surface optimization in growth curves through multivariate analysis

Abstract

A methodology is proposed to jointly model treatments with quantitativelevels measured throughout time by combining the response surface andgrowth curve techniques. The model parameters, which measure the effectthroughout time of the factors related to the second-order response surfacemodel, are estimated. These estimates are made through a suitable transformationthat allows to express the model as a classic MANOVA model,so the traditional hypotheses are formulated and tested. In addition, theoptimality conditions throughout time are established as a set of specificcombination factors by the fitted model. As a final step, two applicationsare analyzed using our proposed model: the first was previously analyzedwith growth curves in another paper, and the second involves two factorsthat are optimized over time.