Methods and formulas for stepwise in Analyze Definitive Screening Design

In This Topic

Forward information criteria procedure
Forward selection procedure
Backward elimination procedure
Stepwise method

Forward information criteria procedure

A method for determining which variables to retain in a model. 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. Minitab displays the results of the analysis for the model with the minimum value of the selected information criterion, either AICc or BIC. In most cases, the procedure continues until one of the following conditions occurs:

The procedure does not find an improvement in 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.

Forward selection procedure

A method for determining which terms to retain in a model. Forward selection adds variables to the model using the same method as the stepwise procedure. Once added, a variable is never removed. The default forward selection procedure ends when none of the candidate variables have a p-value smaller than the value specified in Alpha to enter.

Backward elimination procedure

A method for determining which variables to retain in a model. Backward elimination starts with the model that contains all the terms and then removes terms, one at a time, using the same method as the stepwise procedure. No variable can re-enter the model. The default backward elimination procedure ends when none of the variables included in the model have a p-value greater than the value specified in Alpha to remove. Backward elimination does not proceed if the initial model uses all of the degrees of freedom.

Stepwise method

Performs variable selection by adding or deleting predictors from the existing model based on the F-test. Stepwise is a combination of forward selection and backward elimination procedures. Stepwise selection does not proceed if the initial model uses all of the degrees of freedom.

Variables to remove

Minitab calculates an F-statistic and p-value for each variable in the model. If the model contains j variables, then F for any variable, x_r , is this formula:

Notation

Term	Description
SSE_{(j – X_r )}	SS Error for the model that does not contain x_r
SSE _j	SS Error for the model that contains x_r
MSE _j	MS Error for the model that contains x_r

If the p-value for any variable is greater than the value specified in Alpha to remove, then Minitab removes the variable with the largest p-value from the model, calculates the regression equation, displays the results, and initiates the next step.

Variables to add

If Minitab cannot remove a variable, the procedure attempts to add a variable. Minitab calculates an F-statistic and p-value for each variable that is not in the model. If the model contains j variables, then F for any variable, x_a, is this formula:

Notation

Term	Description
SSE _j	SS Error before x_a is added to the model
SSE_(j+_{X_a )}	SS Error after x_a is added to the model
	Degrees of freedom for variable X_a
MSE_(j+_{X_a )}	MS Error after x_a is added to the model

If the p-value corresponding to the F-statistic for any variable is smaller than the value specified in Alpha to enter, Minitab adds the variable with the smallest p-value to the model, calculates the regression equation, displays the results, then goes to a new step. When no more variables can be entered into or removed from the model, the stepwise procedure ends.