Chapter 32: The GLM Procedure

Overview

The GLM procedure uses the method of least squares to fit general linear models. Among the statistical methods available in PROC GLM are regression, analysis of variance, analysis of covariance, multivariate analysis of variance, and partial correlation.

PROC GLM analyzes data within the framework of General linear models. PROC GLM handles models relating one or several continuous dependent variables to one or several independent variables. The independent variables may be either classification variables, which divide the observations into discrete groups, or continuous variables. Thus, the GLM procedure can be used for many different analyses, including

• simple regression

• multiple regression

• analysis of variance (ANOVA), especially for unbalanced data

• analysis of covariance

• response-surface models

• weighted regression

• polynomial regression

• partial correlation

• multivariate analysis of variance (MANOVA)

• repeated measures analysis of variance

PROC GLM Features

The following list summarizes the features in PROC GLM:

• PROC GLM enables you to specify any degree of interaction (crossed effects) and nested effects. It also provides for polynomial, continuous-by-class, and continuous-nesting-class effects.

• Through the concept of estimability, the GLM procedure can provide tests of hypotheses for the effects of a linear model regardless of the number of missing cells or the extent of confounding. PROC GLM displays the Sum of Squares (SS) associated with each hypothesis tested and, upon request, the form of the estimable functions employed in the test. PROC GLM can produce the general form of all estimable functions.

• The REPEATED statement enables you to specify effects in the model that represent repeated measurements on the same experimental unit for the same response, providing both univariate and multivariate tests of hypotheses.

• The RANDOM statement enables you to specify random effects in the model; expected mean squares are produced for each Type I, Type II, Type III, Type IV, and contrast mean square used in the analysis. Upon request, F tests using appropriate mean squares or linear combinations of mean squares as error terms are performed.

• The ESTIMATE statement enables you to specify an L vector for estimating a linear function of the parameters L ² .

• The CONTRAST statement enables you to specify a contrast vector or matrix for testing the hypothesis that L ² = 0. When specified, the contrasts are also incorporated into analyses using the MANOVA and REPEATED statements.

• The MANOVA statement enables you to specify both the hypothesis effects and the error effect to use for a multivariate analysis of variance.

• PROC GLM can create an output data set containing the input dataset in addition to predicted values, residuals, and other diagnostic measures.

• PROC GLM can be used interactively. After specifying and running a model, a variety of statements can be executed without recomputing the model parameters or sums of squares.

• For analysis involving multiple dependent variables but not the MANOVA or REPEATED statements, a missing value in one dependent variable does not eliminate the observation from the analysis for other dependent variables. PROC GLM automatically groups together those variables that have the same pattern of missing values within the data set or within a BY group . This ensures that the analysis for each dependent variable brings into use all possible observations.

• Experimental graphics are now available with the GLM procedure. For more information, see the ODS Graphics section on page 1846.

PROC GLM Contrasted with Other SAS Procedures

As described previously, PROC GLM can be used for many different analyses and has many special features not available in other SAS procedures. However, for some types of analyses, other procedures are available. As discussed in the PROC GLM for Unbalanced ANOVA and PROC GLM for Quadratic Least Squares Regression sections (beginning on page 1735), sometimes these other procedures are more efficient than PROC GLM. The following procedures perform some of the same analyses as PROC GLM:

ANOVA	performs analysis of variance for balanced designs. The ANOVA procedure is generally more efficient than PROC GLM for these designs.
MIXED	fits mixed linear models by incorporating covariance structures in the model fitting process. Its RANDOM and REPEATED statements are similar to those in PROC GLM but offer different functionalities.
NESTED	performs analysis of variance and estimates variance components for nested random models. The NESTED procedure is generally more efficient than PROC GLM for these models.
NPAR1WAY	performs nonparametric one-way analysis of rank scores. This can also be done using the RANK procedure and PROC GLM.
REG	performs simple linear regression. The REG procedure allows several MODEL statements and gives additional regression diagnostics, especially for detection of collinearity. PROC REG also creates plots of model summary statistics and regression diagnostics.
RSREG	performs quadratic response-surface regression, and canonical and ridge analysis. The RSREG procedure is generally recommended for data from a response surface experiment.
TTEST	compares the means of two groups of observations. Also, tests for equality of variances for the two groups are available. The TTEST procedure is usually more efficient than PROC GLM for this type of data.
VARCOMP	estimates variance components for a general linear model.