Is it possible to have one factor which is not significant in a response surface model but the quadratic term for the same factor is?I'm trying to model one of my responses in JMP which has been evaluated using a DoE CCD design. In the DoE model, I have one factor which is not significant to the model around this response (p >0.05) but the quadratic term is significant (p<0.05). According to the Effect Hereditary Principle, in order for an interaction to be significant, at least one of its parent factors should be significant. Does this also apply for quadratic terms? How should this be interpreted?
DOERe: Is it possible to have one factor which is not significant in a response surface model but the quadratic term for the same factor is?Effect heredity is a guideline/concept/principle, not a hard and fast rule. It's a principle to help guide us in how we may choose to characterize systems with linear in the parameters models. So it's entirely possible for a main effect to not be significant but a quadratic effect for the same factor is significant. Here's a simulated example. Note the perfect parabola for X1. And the resultant Fit Model analysis showing only the X1*X1 term is significant.
Re: Is it possible to have one factor which is not significant in a response surface model but the quadratic term for the same factor is?Adding to @P_Bartell, this situation brings up the topic of 'model hierarchy.' The presence of the squared term causes a hierarchy. X is present in X*X. As such, it is strongly recommended that you maintain the hierarchy. That is to say, If the X*X term is significant but the X term is not significant, keep both terms in the model.
JMP checks for such cases and warns you if removing a term will affect the hierarchy. JMP will allow you to proceed, but it is not recommended.
Re: Is it possible to have one factor which is not significant in a response surface model but the quadratic term for the same factor is?Mark is correct as this is effect hierarchy. Think of it this way, if you are going to "model" the curvature of the factor (X*X) then you will certainly need to manage X. Whether it contributes to the prediction precision or not is really of little consequence.
