ON FITTING EQUATIONS TO SENSORY DATA: A POINT OF VIEW, AND A PARADOX IN MODELING AND OPTIMIZING

When fitting equations to data relating ingredients or factor scores to subjective ratings, there are at least two methods to create the equations. One method, (linear) forces in linear terms and allows additional quadratic and interaction terms. The other method, (quadratic) forces in linear and quadratic terms, and then permits cross-terms to enter. The two methods produce contradictory results. The first (and expected) contradiction is that the quadratic model shows optimum levels in the middle range of the levels tested for some, but not all, ingredients. The second (and unexpected) contradiction is that the linear method (which usually does not incorporate many additional terms) generates better validation predictions for hold-out samples than does the quadratic method. The differences between the optimum generated by the linear model and the optimum generated by the quadratic model can be quite substantial in terms of expected liking, sensory profile, and image profile.