Analyze Response Surface Design - Hierarchy
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Stat > DOE > Response Surface > Analyze Response Surface Design > Stepwise > Hierarchy

Use to control how Minitab enforces model hierarchy during a stepwise procedure. In a hierarchical model, if a higher-order term is included, all lower-order terms that comprise the higher-order term also appear in the model. For example, a model that includes the interaction term A*B*C is hierarchical if it includes the following main effects and lower-order interactions: A, B, C, A*B, and B*C.

Response surface design models must be hierarchical if you want to produce an equation in uncoded (or natural) units. However, weigh that consideration against the fact that models that contain too many terms can be relatively imprecise and can reduce the ability to predict the values of new observations.

Consider the following tips.

·    Fit a hierarchical model first. You can remove insignificant terms later.

·    If your model contains categorical variables, the results are easier to interpret if the categorical terms, at least, are hierarchical.

Dialog box items

Hierarchical model: Choose whether the stepwise procedure must produce a hierarchical model.

Require a hierarchical model at each step: Minitab can only add terms at each step that maintain hierarchy.

Add terms at the end to make the model hierarchical: Initially, Minitab follows the standard rules of the stepwise procedure. At the final step, Minitab adds all terms that are necessary to produce a hierarchical model even if their p-values are greater than the alpha-to-enter.

Do not require a hierarchical model: The final model can be non-hierarchical. Minitab will add and remove terms based only on the rules of the stepwise procedure.

Require hierarchy for the following terms: If you require a hierarchical model, choose the types of terms that must be hierarchical.

All terms: Terms that include continuous and/or categorical variables must be hierarchical.

Terms with categorical predictors: Only terms that include categorical variables must be hierarchical.

How many terms can enter at each step: If you require hierarchy at each step, choose the number of terms that Minitab can add at each step in order to maintain hierarchy.

At most one term can enter at each step: An interaction or power term can enter the model only if hierarchy is maintained when adding that single term. All lower-order terms that comprise the interaction or power term must already be in the model.

Extra terms can enter to maintain hierarchy: An interaction or power term can enter the model even if hierarchy is not maintained. However, all additional terms that are necessary to produce a hierarchical model are also added even if their p-values are greater than the alpha-to-enter.