Specifying reduced models
main topic 

You can fit reduced models. For example, suppose you have a three factor design, with factors, A, B, and C. The full model would include all one factor terms: A, B, C, all two-factor interactions: A * B, A * C, B * C, and the three-factor interaction: A *  B * C. It becomes a reduced model by omitting terms. You might reduce a model if terms are not significant or if you need additional error degrees of freedom and you can assume that certain terms are zero. For this example, the model with terms A B C A * B is a reduced three-factor model.

One rule about specifying reduced models is that they must be hierarchical. That is, for a term to be in the model, all lower order terms contained in it must also be in the model. For example, suppose there is a model with four factors: A, B, C, and D. If the term A * B * C is in the model then the terms A B C A * B A * C B * C must also be in the model, though any terms with D do not have to be in the model. The hierarchical structure applies to nesting as well. If B (A) is in the model, then A must be also.

Because models can be quite long and tedious to type, two shortcuts have been provided. A vertical bar indicates crossed factors, and a minus sign removes terms.

Long form

Short form

A B C A * B A * C B * C A * B * C

A | B | C

A B C A * B A * C B * C

A | B | C - A * B * C

A B C B * C E

A B | C E

A B C D A * B A * C A * D B * C B * D C * D A * B * D A * C * D B * C * D

A | B | C | D - A * B * C - A * B * C * D

A B (A) C A * C B * C

A | B (A) | C

In general, all crossings are done for factors separated by bars unless the cross results in an illegal term. For example, in the last example, the potential term A * B (A) is illegal and Minitab automatically omits it. If a factor is nested, you must indicate this when using the vertical bar, as in the last example with the term B (A).