The GLIMMIX Procedure

Type III Tests of Fixed Effects

The "Type III Tests of Fixed Effects" table contains hypothesis tests for the significance of each of the fixed effects specified in the MODEL statement. By default, PROC GLIMMIX computes these tests by first constructing a Type III bold upper L matrix for each effect; see Chapter 16, The Four Types of Estimable Functions. The bold upper L matrix is then used to construct the test statistic

upper F equals StartFraction ModifyingAbove bold-italic beta With caret prime bold upper L prime left-parenthesis bold upper L bold upper Q bold upper L prime right-parenthesis Superscript negative 1 Baseline bold upper L ModifyingAbove bold-italic beta With caret Over normal r normal a normal n normal k left-parenthesis bold upper L bold upper Q bold upper L prime right-parenthesis EndFraction

where the matrix bold upper Q depends on the estimation method and options. For example, in a GLMM, the default is bold upper Q equals left-parenthesis bold upper X prime bold upper V left-parenthesis ModifyingAbove bold-italic theta With caret right-parenthesis Superscript negative 1 Baseline bold upper X right-parenthesis Superscript minus, where bold upper V left-parenthesis bold-italic theta right-parenthesis is the marginal variance of the pseudo-response. If you specify the DDFM=KENWARDROGER option, bold upper Q is the estimated variance matrix of the fixed effects, adjusted by the method of Kenward and Roger (1997). If the EMPIRICAL= option is in effect, bold upper Q corresponds to the selected sandwich estimator.

You can use the HTYPE= option in the MODEL statement to obtain tables of Type I (sequential) tests and Type II (adjusted) tests in addition to or instead of the table of Type III (partial) tests.

The ODS names of the "Type I Tests of Fixed Effects" through the "Type III Tests of Fixed Effects" tables are Tests1 through Tests3, respectively.

Last updated: December 09, 2022