The Model

The GLM Multivariate procedure is based on the general linear model, in which factors and covariates are assumed to have linear relationships to the dependent variables.

Fixed Factors. Categorical predictors should be selected as factors in the model. Each level of a factor can have a different linear effect on the value of the dependent variables. The GLM Multivariate procedure assumes that all the model factors are fixed; that is, they are generally thought of as variables whose values of interest are all represented in the data file, usually by design.

Covariates. Scale predictors should be selected as covariates in the model. Within combinations of factor levels (or cells), values of covariates are assumed to be linearly correlated with values of the dependent variables.

Interactions. By default, the GLM Multivariate procedure produces a model with all factorial interactions, which means that each combination of factor levels can have a different linear effect on the dependent variable. Additionally, you may specify factor-covariate interactions, if you believe that the linear relationship between a covariate and the dependent variables changes for different levels of a factor.

For the purposes of testing hypotheses concerning parameter estimates, the GLM Multivariate procedure assumes:

• The values of errors are independent of each other across observations and the independent variables in the model. Good study design generally avoids violation of this assumption.
• The covariance of dependent variables is constant across cells. This can be particularly important when there are unequal cell sizes; that is, different numbers of observations across factor-level combinations.
• Across the dependent variables, the errors have a multivariate normal distribution with a mean of 0.

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