Perform stepwise regression for Analyze Response Surface Design

Stepwise removes and adds terms to the model for the purpose of identifying a useful subset of the terms. If you choose a stepwise procedure, the terms that you specify in the Terms sub-dialog box are candidates for the final model. For more information, go to Using stepwise regression and best subsets regression.

Specify which information criterion to use in forward selection.

Both AICc and BIC assess the likelihood of the model and then apply a penalty for adding terms to the model. The penalty reduces the tendency to overfit the model to the sample data. This reduction can yield a model that performs better in general.

As a general guideline, when the number of parameters is small relative to the sample size, BIC has a larger penalty for the addition of each parameter than AICc. In these cases, the model that minimizes BIC tends to be smaller than the model that minimizes AICc.

In some common cases, such as screening designs, the number of parameters is usually large relative to the sample size. In these cases, the model that minimizes AICc tends to be smaller than the model that minimizes BIC. For example, for a 13-run definitive screening design, the model that minimizes AICc will tend to be smaller than the model that minimizes BIC among the set of models with 6 or more parameters.

For more information on AICc and BIC, see Burnham and Anderson.¹

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 Terms sub-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 must also include the terms: A, B, C, A*B, A*C, and B*C to be hierarchical.

Response surface models must be hierarchical if you want to produce an equation in uncoded 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.

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. If you select this option when the Method is Forward information criteria, Minitab displays an error. To get a hierarchical model that minimizes the criterion among the models in the steps, select Require a hierarchical model at each step.
• 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.