The GLIMMIX Procedure

Containment Degrees of Freedom Approximation

The DDFM= CONTAIN method is carried out as follows: Denote the fixed effect in question as A and search the G-side random effect list for the effects that syntactically contain A. For example, the effect B(A) contains A, but the effect C does not, even if it has the same levels as B(A).

Among the random effects that contain A, compute their rank contributions to the $[\mb{X\, \, \,  Z}]$ matrix (in order). The denominator degrees of freedom that is assigned to A is the smallest of these rank contributions. If no effects are found, the denominator degrees of freedom for A is set equal to the residual degrees of freedom, $n - \mr{rank}[\mb{X\, \, \,  Z}]$. This choice of degrees of freedom is the same as for the tests performed for balanced split-plot designs and should be adequate for moderately unbalanced designs.

Note: If you have a $\bZ $ matrix with a large number of columns, the overall memory requirements and the computing time after convergence can be substantial for the containment method. In this case, you might want to use a different degrees-of-freedom method, such as DDFM=RESIDUAL, DDFM=NONE, or DDFM=BETWITHIN.