Models with Crossed, Interaction, or Polynomial Terms

Some models, especially those associated with experimental designs, involve interaction terms. For continuous factors, these are products of the columns representing the effects. For nominal and ordinal factors, interactions are defined by model terms that involve products of terms representing the categorical levels.

When there are interaction terms, you often want to impose a restriction on the model selection process so that lower-order components of higher-order effects are included in the model. This is suggested by the principle of Effect Heredity. See the Design of Experiments Guide. For example, if a two-way interaction is included in a model, its component main effects (precedents) should be included as well.

Example of the Combine Rule

1.	Select Help > Sample Data Library and open Reactor.jmp.

2.	Select Analyze > Fit Model.

3.	Select Y and click Y.

4.	In the Degree box, type 2.

5.	Select F, Ct, A, T, and Cn and click Macros > Factorial to Degree.

6.	For Personality, select Stepwise.

7.	Click Run.

Initial Current Estimates Report Using Combine Rule

The model in Initial Current Estimates Report Using Combine Rule contains all terms for up to two-factor interactions for the five continuous factors. The Combine, Restrict, and Whole Effects rules described in Rules enable you to control entry of interaction terms.

For example, using the Combine rule, the interaction term Ct*T is grouped with its precedent terms Ct and T. The Ct*T interaction is only entered based on the p-value from a joint F test. Because Ct*T can only be entered based on a 3 degree of freedom joint F test, its nDF value is recorded as 3. Click Step once to see that Ct*T is entered, along with Ct and T.

Current Estimates Report Using Combine Rule, One Step

When there are significant interaction terms, often several terms enter at the same step. If the Step button is clicked once, Ct*T is entered along with its two contained effects Ct and T. However, a step back is not symmetric because a crossed term can be removed without removing its two component terms. Notice that Ct and T now each have 2 degrees of freedom. This is because if Stepwise removes Ct or T, it must also remove Ct*T. If you change the Direction to Backward and click Step, Ct*T is removed and the degrees of freedom for Ct and T change to 1.