Specify the stepwise regression method, parameters, and the details to show. The changes you make to the defaults remain until you change them again, even after you exit Minitab. Minitab uses the settings you specify here each time you use one of the following analyses:
Mixture designs are different from the other tools in 2 ways. If you select Forward information criteria as the default method, then the default method for mixture designs remains None. Also, the results for mixture designs always show the same details.
- Default method
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- None: Fit with the model with all the terms that you specify in Terms.
- Forward information criteria: The forward information criteria procedure adds the term with the lowest p-value to the model at each step. Additional terms can enter the model in 1 step if the settings for the analysis allow consideration of non-hierarchical terms but require each model to be hierarchical. Minitab calculates the information criteria for each step. In most cases, the procedure continues until one of the following conditions occurs:
- The procedure does not find a new minimum of the criterion for 8 consecutive steps.
- The procedure fits the full model.
- The procedure fits a model that leaves 1 degree of freedom for error.
If you specify settings for the procedure that
require a hierarchical model at each step and allow only one term
to enter at a time, then the procedure continues until it either fits the full model or fits a model that leaves 1 degree of freedom for error. Minitab displays the results of the analysis for the model with the minimum value of the selected information criterion, either AICc or BIC.
- Stepwise: Start with an empty model, then add or remove a term for each step. You can specify an initial set of terms to include in the model.
- Forward selection: Start with an empty model, then add the most significant potential term to the model for each step.
- Backward elimination: Start with all potential terms in the model, then remove the least significant term for each step.
- Forward Information
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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
- Stepwise Parameters
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- Alpha to enter: Specify the criterion for entering a new term in the model.
- Alpha to remove: Specify the criterion for removing term from the model.
- Forward Selection Parameter
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- Alpha to enter: Specify the criterion for entering a new term in the model.
- Backward Elimination Parameter
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- Alpha to remove: Specify the criterion for removing term from the model.
- Display the table of model selection details
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Display information about the stepwise procedure in a table.
- Details about the method: Display the type of stepwise procedure and the alpha values that are used to add and/or remove a term from the model.
- Include details for each step: Display the coefficients, p-values, Mallows' Cp, and model summary statistics for each step of the procedure.
1 Burnham, K. P., & Anderson, D. R. (2004). Multimodel inference: Understanding AIC and BIC in model selection.
Sociological Methods & Research, 33(2), 261-304. doi:10.1177/0049124104268644
