Building a Model

Here is the form for a mixed model: .

In this equation, y represents univariate data, is an unknown vector of fixed effects with known model matrix X, is an unknown vector of random effects with known model matrix Z, and is an unknown random error vector.

Using the Mixed Models task, you can add fixed, random, and repeated effects to your model.

By default, no effects are specified, which results in the task fitting an intercept-only model.

To specify a model effect, you must assign at least one variable to the Classification variables role or the Continuous variables role. On the Model tab, click to open the Model Effects Builder.

In the Mixed Models task, you can create fixed effects, random effects, and repeated effects. (You can have only one repeated effect.) These effects are added to the model in the order in which they appear on the Model tab.

For fixed effects, the intercept is included by default. To add additional fixed effects, click to open the Fixed Effects Builder.

You can have multiple random effects in the model.

To create a random effect, click to open the Random Effects Builder. In the Random Effects Builder, you can create these types of single effects: a main effect, a crossed effect, an effect with a polynomial degree of n, and a nested effect.

You can also create a subject effect or a group effect. Specifying a subject effect is equivalent to nesting all other random effects in the subject effect. The group effect is an effect that specifies heterogeneity in the covariance structure of the R matrix. All observations that have the same level of the group effect have the same covariance parameters.

You can have only one repeated effect in the model. Only classification variables can be used to create a repeated effect.

To create a repeated effect, click to open the Repeated Effects Builder. In the Repeated Effects Builder, you can create these types of single effects: a main effect, a crossed effect, an effect with a polynomial degree of n, and a nested effect. Y

You can also create a subject effect or a group effect. Specifying a subject effect is equivalent to nesting all other random effects in the subject effect. The group effect is an effect that specifies heterogeneity in the covariance structure of the R matrix. All observations that have the same level of the group effect have the same covariance parameters.

For example, if you select Age, click Polynomial Degree=N, and specify 3 as the value of N, the Age*Age*Age effect is created.

Nested effects are specified by following a main effect or crossed effect with a classification variable or list of classification variables enclosed in parentheses. Here are examples of nested effects: B(A), C(B*A), D*E(C*B*A). In this example, B(A) is read "B within A."

For example, if you select the Age and Height variables and then click Two-Way Factorial, the Age*Height effect is created.

For example, if you select the Height, Weight, and Age variables and then click Full Factorial, these model effects are created: Age, Height, Weight, Age*Height, Age*Weight, Height*Weight, and Age*Height*Weight.

For example, if you select the Height, Weight, and Age variables, click N-way Factorial, and then specify the value of N as 2, these model effects are created: Age, Height, Weight, Age*Height, Age*Weight, and Height*Weight. If N is set to a value greater than the number of variables in the model, N is effectively set to the number of variables.

For example, if you select the Age and Height variables, click Polynomial Order=N, and specify 3 as the value of N, these model effects are created: Age, Age*Age, Age*Age*Age, Height, Height*Height, and Height*Height*Height.