Fitting Linear Models > Model Specification > Model Specification Templates
Publication date: 07/08/2024

Model Specification Templates

To obtain specific types of models, enter the correct effects in the Construct Model Effects panel of the Fit Model launch window.

In this section, the model effects X and Z represent continuous columns and the model effects A, B, and C represent nominal or ordinal columns.

Basic steps for constructing model effects are available for the following models:

Simple Linear Regression

Polynomial in X to Degree k

Polynomial in X and Z to Degree k

Multiple Linear Regression

One-Way Analysis of Variance

Two-Way Analysis of Variance

Two-Way Analysis of Variance with Interaction

Three-Way Full Factorial

Analysis of Covariance, Equal Slopes

Analysis of Covariance, Unequal Slopes

Two-Factor Nested Random Effects Model

Three-Factor Fully Nested Random Effects Model

Simple Split Plot or Repeated Measures Model

Two-Factor Response Surface Model

Knotted Spline Effect

Simple Linear Regression

Effects to be entered: X

1. In the Select Columns list, select X.

2. Click Add.

Note: For an example of a simple linear regression model, see Example of Simple Linear Regression.

Polynomial in X to Degree k

Effects to be entered: X, X*X,..., Xk

1. Type k into the text box for Degree.

2. In the Select Columns list, select X.

3. Select Macros > Polynomial to Degree.

Note: For an example of a polynomial model in X to degree k, see Example of a Polynomial Effects Model.

Polynomial in X and Z to Degree k

Effects to be entered: X, X*X,..., Xk, Z, Z*Z,..., Zk

1. Type k into the text box for Degree.

2. In the Select Columns list, select X and Z.

3. Select Macros > Polynomial to Degree.

Multiple Linear Regression

Effects to be entered: Selected columns

1. In the Select Columns list, select the continuous effects of interest.

2. Click Add.

Note: For an example of multiple linear regression with several predictors, see Example of a Regression Analysis Using Fit Model.

One-Way Analysis of Variance

Effects to be entered: A

1. In the Select Columns list, select one nominal or ordinal effect, A.

2. Click Add.

Note: For an example, of one-way analysis of variance (ANOVA), see Example of One-Way Analysis of Variance.

Two-Way Analysis of Variance

Effects to be entered: A, B

1. In the Select Columns list, select two nominal or ordinal effects, A and B.

2. Click Add.

Note: For an example of a two-way analysis of variance model, see Example of Two-Way Analysis of Variance.

Two-Way Analysis of Variance with Interaction

Effects to be entered: A, B, A*B

1. In the Select Columns list, select two nominal or ordinal effects, A and B.

2. Select Macros > Full Factorial.

Or:

1. In the Select Columns list, select two nominal or ordinal effects, A and B.

2. Click Add.

3. In the Select Columns list, select A and B again and click Cross.

Note: For an example of a two-way analysis of variance model with an interaction effect, see Example of Two-Way Analysis of Variance with an Interaction.

Three-Way Full Factorial

Effects to be entered: A, B, C, A*B, A*C, B*C, A*B*C

1. In the Select Columns list, select three nominal or ordinal effects, A, B, and C.

2. Select Macros > Full Factorial.

Note: For an example of a three-way full factorial model, see Example of a Three-Way Full Factorial Model.

Analysis of Covariance, Equal Slopes

Test for the effect of A with X as a covariate. Suppose that you have reason to believe that the effect of X on the response does not depend on the level of A.

Effects to be entered: A, X

1. In the Select Columns list, select one nominal or ordinal effect, A, and one continuous effect, X.

2. Click Add.

Note: For an example of analysis of covariance with equal slopes, see Example of Analysis of Covariance with Equal Slopes.

Analysis of Covariance, Unequal Slopes

Test for the effect of A with X as a covariate. Suppose that you construct your model to allow the possibility that the effect of X on the response depends on the level of A.

Effects to be entered: A, X, A*X

1. In the Select Columns list, select one nominal or ordinal effect, A, and one continuous effect, X.

2. Select Macros > Full Factorial.

Or:

1. In the Select Columns list, select one nominal or ordinal effect, A, and one continuous effect, X.

2. Click Add.

3. In the Select Columns list, select A and X again and click Cross.

Note: For an example of analysis of covariance with unequal slopes, see Example of Analysis of Covariance with Unequal Slopes.

Two-Factor Nested Random Effects Model

Consider a model with two factors, A and B, but where B is nested within A. Although there are situations where a nested effect is treated as a fixed effect, in most situations a nested effect is treated as a random effect. For this reason, in the model described below, the nested effect is entered as a random effect.

Effects to be entered: A, B[A]&Random

1. In the Select Columns list, select two nominal or ordinal effects, A and B.

2. Click Add.

3. To nest B within A: In the Construct Model Effects list, select B. In the Select Columns list, select A. The two effects should be highlighted.

4. Click Nest.

5. With B[A] highlighted in the Construct Model Effects list, select Attributes > Random Effect.

Note: For an example of a two-factor nested random effects model, see Example of a Two-Factor Nested Random Effects Model.

Three-Factor Fully Nested Random Effects Model

Consider a model with three factors, A, B, and C, but where B is nested within A and C is nested within both A and B. Also consider B and C to be random effects.

Effects to be entered: A, B[A]&Random, C[A,B]&Random

1. In the Select Columns list, select three nominal or ordinal effects, A, B, and C.

2. Click Add.

3. To nest B within A: In the Construct Model Effects list, select B. In the Select Columns list, select A. The two effects should be highlighted.

4. Click Nest.

5. To nest C within A and B: In the Construct Model Effects list, select C. In the Select Columns list, select A and B. The three effects should be highlighted.

6. Click Nest.

7. With both B[A] and C[A,B] highlighted in the Construct Model Effects list, select Attributes > Random Effect.

Simple Split Plot or Repeated Measures Model

Effects to be entered: A, B[A]&Random, C, C*A where A is the whole plot variable, B[A] is the whole plot ID, and C is the split plot, or repeated measures, variable.

1. In the Select Columns list, select two nominal or ordinal effects, A and B.

2. Click Add.

3. To nest B within A: In the Construct Model Effects list, select B. In the Select Columns list, select A. The two effects should be highlighted.

4. Click Nest.

5. In the Construct Model Effects list, select B[A].

6. Select Attributes > Random Effect.

7. In the Select Columns list, select a third nominal or ordinal effect, C.

8. Click Add.

9. In the Construct Model Effects list, select C. In the Select Columns list, click A. Both effects should be highlighted.

10. Click Cross.

Note: For an example of a simple repeated measures model, see Example of a Simple Repeated Measures Model.

Two-Factor Response Surface Model

Effects to be entered: X&RS, Z&RS, X*X, X*Z, Z*Z

1. In the Select Columns list, select two continuous effects, X and Z.

2. Select Macros > Response Surface.

Knotted Spline Effect

Effects to be entered: X&Knotted

1. In the Select Columns list, select a continuous effect, X.

2. Click Add.

3. Select X in the Construct Model Effects list.

4. Select Attributes > Knotted Spline Effect.

5. In the window that appears, select between the default number of equally spaced knots, specifying a different number of equally spaced knots, or specifying a set of custom knot points.

6. Click OK.

Note: For an example of a model with a knotted spline effect, see Example of Using a Knotted Spline Effect.

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