You can determine how Minitab enforces model hierarchy during a stepwise procedure. The Hierarchy button is disabled if you specify a non-hierarchical model in the Model dialog box.
In a hierarchical model, all lower-order terms that comprise the higher-order terms also appear in the model. For example, a model that includes the interaction term A*B*C is hierarchical if it includes these terms: A, B, C, A*B, A*C, and B*C.
Models can be non-hierarchical. Generally, you can remove lower order terms if they are insignificant, unless subject area knowledge suggests that you include them. 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 you standardize your continuous predictors, fit a hierarchical model to produce an equation in uncoded (or natural) units.
- If your model contains categorical variables, the results are easier to interpret if the categorical terms, at least, are hierarchical.
- Hierarchical model
- Choose whether the stepwise procedure must produce a hierarchical model.
- Require a hierarchical model at each step: Minitab can only add or remove terms 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 the terms that produce a hierarchical model, even if their p-values are greater than the Alpha to enter value.
- 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: A higher-order term can enter the model only if hierarchy is maintained when adding that single term. All lower-order terms that comprise the higher-order must already be in the model.
- Extra terms can enter to maintain hierarchy: A higher-order term can enter the model even if it produces a non-hierarchical model. However, the terms that are necessary to produce a hierarchical model are also added, even if their p-values are greater than the Alpha to enter value.