When the default GLM parameterization is used for CLASS predictors, the test of a model effect in the Analysis of (GEE) Parameter Estimates table is a test that the individual parameter is zero while the test in the Type 3 (GEE) analysis table is a test of a type 3 hypothesis. With GLM parameterization, the type3 hypothesis for an effect might involve many other parameters in the model, such as parameters in interactions involving the effect. To see the form of the type 3 hypothesis for a given effect, run the same model in PROC GLM (omit the REPEATED statement if used) and specify the E and E3 options in the MODEL statement of PROC GLM. Ignore all PROC GLM results other than the Estimable Functions tables. The E option shows the general form of the estimable functions, and the E3 option shows the form of the type 3 hypotheses that is tested by the TYPE3 option in PROC GENMOD and displayed in the Type 3 (GEE) Analysis table. See The Four Types of Estimable Functions chapter in the SAS/STAT User's Guide, which discusses the interpretation and use of the tables produced by the E and E3 options. See, in particular, the Estimability section of the chapter, which includes an Examples subsection.

When full-rank parameterization such as reference parameterization (PARAM=REF) is used, the TYPE3 option produces a table of joint tests. The joint test for an effect is a test that all parameters associated with that effect are zero. For more on type 3 and joint tests, see Type 3 Analysis in the Details section of the GENMOD documentation (SAS Note 22930).

Even when the type 3 test of an effect is only a test of the effect's single parameter, the results might differ because of different test types. The test in the Parameter Estimates table is a Wald chi-square test (standard normal (Z) equivalent test for GEE analyses). The test in the Type 3 analysis/Joint Tests table is, by default, a likelihood ratio (LR) test (score test for GEE analyses). The Wald test is known to be less powerful than the LR test when the effect is large. Under these circumstances, the Wald statistic becomes too small. Generally, the LR test is preferred. In GEE analyses when the number of clusters is small, the Wald test can be too liberal. The score test is generally more conservative. Use the WALD option in the MODEL statement to request Wald tests in the Type 3 analysis table.

If you use the CONTRAST statement to perform a test on a single parameter, the result might also differ from the corresponding test in the Parameter Estimates table because of test type differences. By default, the test in the CONTRAST statement is a likelihood ratio test (score test for GEE analyses) while the test in the Parameter Estimates table is a Wald test. In GEE analyses, the Z statistic is the square root of a Wald statistic and has the same p-value as the Wald statistic. You can request a Wald test of your contrast by specifying the WALD option in the CONTRAST statement.

If you use the ESTIMATE statement to test a type 3 hypothesis, the result might differ from the corresponding test in the Type 3 analysis table because of test type differences. The test in the ESTIMATE statement is a Wald test while the test in the Type 3 analysis table is, by default, a LR test (score test for GEE analyses). You can request Wald tests in the Type 3 analysis table by specifying the WALD option in the MODEL statement.

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