Table 1.

The denominator degrees of freedom of GLMM Wald F test by different approximation methods in the simulations under the framework of CRTs

Methods	Estimated denominator degrees of freedom
Residual	${\displaystyle \sum _{i=1}^K}{n}_i-2$
Containment	${\displaystyle \sum _{i=1}^K}{n}_i-K$
Between-Within	K − 2
Satterthwaite	d, estimated from data
Kenward-Roger	d, estimated from data