Specify the options for the stepwise regression analysis of your factorial 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.
The terms that are included in the final model can depend on hierarchy restrictions for models. For more information, see the topic on Hierarchy below.
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.
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.