Poisson Regression - Hierarchy in Stepwise
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Stat > Regression > Poisson Regression > Fit Poisson Model > Stepwise > Hierarchy

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

Models can be non-hierarchical. Generally, it is valid to remove the 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 predictors, it is recommended that you use a hierarchical model.

·    If your model contains categorical predictors, it is recommended that at least the categorical terms are hierarchical because the results are easier to interpret.

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 or remove 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 predictors must be hierarchical.

Terms with categorical predictors: Only terms that include categorical predictors 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.