The GLM Procedure

RANDOM Statement

RANDOM effects </ options> ;

When some model effects are random (that is, assumed to be sampled from a normal population of effects), you can specify these effects in the RANDOM statement in order to compute the expected values of mean squares for various model effects and contrasts and, optionally, to perform random effects analysis of variance tests. You can use as many RANDOM statements as you want, provided that they appear after the MODEL statement. If you use a CONTRAST statement with a RANDOM statement and you want to obtain the expected mean squares for the contrast hypothesis, you must enter the CONTRAST statement before the RANDOM statement.

Note: PROC GLM uses only the information pertaining to expected mean squares when you specify the TEST option in the RANDOM statement and, even then, only in the extra F tests produced by the RANDOM statement. Other features in the GLM procedure—including the results of the LSMEANS and ESTIMATE statements—assume that all effects are fixed, so that all tests and estimability checks for these statements are based on a fixed-effects model, even when you use a RANDOM statement. Therefore, you should use the MIXED procedure to compute tests involving these features that take the random effects into account; see the section PROC GLM versus PROC MIXED for Random-Effects Analysis and Chapter 63: The MIXED Procedure, for more information.

When you use the RANDOM statement, by default the GLM procedure produces the Type III expected mean squares for model effects and for contrasts specified before the RANDOM statement in the program statements. In order to obtain expected values for other types of mean squares, you need to specify which types of mean squares are of interest in the MODEL statement. See the section Computing Type I, II, and IV Expected Mean Squares for more information.

The list of effects in the RANDOM statement should contain one or more of the pure classification effects specified in the MODEL statement (that is, main effects, crossed effects, or nested effects involving only classification variables). The coefficients corresponding to each effect specified are assumed to be normally and independently distributed with common variance. Levels in different effects are assumed to be independent.

You can specify the following options in the RANDOM statement after a slash (/):

Q

displays all quadratic forms in the fixed effects that appear in the expected mean squares. For some designs, such as large mixed-level factorials, the Q option might generate a substantial amount of output.

TEST

performs hypothesis tests for each effect specified in the model, using appropriate error terms as determined by the expected mean squares.

Caution: PROC GLM does not automatically declare interactions to be random when the effects in the interaction are declared random. For example,

random a b / test;

does not produce the same expected mean squares or tests as

random a b a*b / test;

To ensure correct tests, you need to list all random interactions and random main effects in the RANDOM statement.

See the section Random-Effects Analysis for more information about the calculation of expected mean squares and tests and on the similarities and differences between the GLM and MIXED procedures. See Chapter 5: Introduction to Analysis of Variance Procedures, and Chapter 63: The MIXED Procedure, for more information about random effects.