GLM Univariate Model

The GLM Univariate procedure is based on the General Linear Model procedure, in which factors and covariates are assumed to have a linear relationship to the dependent variable.

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 variable.

Fixed-effects factors are generally thought of as variables whose values of interest are all represented in the data file.
Random-effects factors are variables whose values in the data file can be considered a random sample from a larger population of values. They are useful for explaining excess variability in the dependent variable.

For example, a grocery store chain is interested in the effects of five different types of coupons on customer spending. At several store locations, these coupons are handed out to customers who frequent that location; one coupon selected at random to each customer.

The type of coupon is a fixed effect because the company is interested in those particular coupons. The store location is a random effect because the locations used are a sample from the larger population of interest, and while there is likely to be store-to-store variation in customer spending, the company is not directly interested in that variation in the context of this problem.

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 Univariate 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 variable changes for different levels of a factor.

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

The values of errors are independent of each other and the variables in the model. Good study design generally avoids violation of this assumption.
The variability of errors 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.
The errors have a normal distribution with a mean of 0.