General Linear Model (GLM) and MANOVA (GLM command)

MANOVA, the other generalized procedure for analysis of variance and covariance, is available only in syntax. The major distinction between GLM and MANOVA in terms of statistical design and functionality is that GLM uses a non-full-rank, or overparameterized, indicator variable approach to parameterization of linear models instead of the full-rank reparameterization approach that is used in MANOVA. GLM employs a generalized inverse approach and employs aliasing of redundant parameters to 0. These processes employed by GLM allow greater flexibility in handling a variety of data situations, particularly situations involving empty cells. GLM offers the following features that are unavailable in MANOVA:

• Identification of the general forms of estimable functions.
• Identification of forms of estimable functions that are specific to four types of sums of squares (Types I–IV).
• Tests that use the four types of sums of squares, including Type IV, specifically designed for situations involving empty cells.
• Flexible specification of general comparisons among parameters, using the syntax subcommands LMATRIX, MMATRIX, and KMATRIX; sets of contrasts can be specified that involve any number of orthogonal or nonorthogonal linear combinations.
• Nonorthogonal contrasts for within-subjects factors (using the syntax subcommand WSFACTORS).
• Tests against nonzero null hypotheses, using the syntax subcommand KMATRIX.
• Feature where estimated marginal means (EMMEANS) and standard errors (adjusted for other factors and covariates) are available for all between-subjects and within-subjects factor combinations in the original variable metrics.
• Uncorrected pairwise comparisons among estimated marginal means for any main effect in the model, for both between- and within-subjects factors.
• Feature where post hoc or multiple comparison tests for unadjusted one-way factor means are available for between-subjects factors in ANOVA designs; twenty different types of comparisons are offered.
• Weighted least squares (WLS) estimation, including saving of weighted predicted values and residuals.
• Automatic handling of random effects in random-effects models and mixed models, including generation of expected mean squares and automatic assignment of proper error terms.
• Specification of several types of nested models via dialog boxes with proper use of the interaction operator (*), due to the nonreparameterized approach.
• Univariate homogeneity-of-variance assumption, tested by using the Levene test.
• Between-subjects factors that do not require specification of levels.
• Profile (interaction) plots of estimated marginal means for visual exploration of interactions involving combinations of between-subjects and/or within-subjects factors.
• Saving of casewise temporary variables for model diagnosis: unstandardized (raw) and weighted unstandarized predicted values; unstandardized, weighted unstandardized, standardized, Studentized, and deleted residuals; standard error of prediction, Cook's distance, leverage.
• Saving of a datafile in IBM® SPSS® Statistics format with parameter estimates and their degrees of freedom and significance level.

To simplify the presentation, GLM reference material is divided into three sections: univariate designs with one dependent variable, multivariate designs with several interrelated dependent variables, and repeated measures designs, in which the dependent variables represent the same types of measurements, taken at more than one time.

The full syntax diagram for GLM is presented here. The following GLM sections include partial syntax diagrams, showing the subcommands and specifications that are discussed in that section. Individually, those diagrams are incomplete. Subcommands that are listed for univariate designs are available for any analysis, and subcommands that are listed for multivariate designs can be used in any multivariate analysis, including repeated measures.