I can't tell you for sure which one to use, you will have to make the final decision. However, if you haven't already, I would suggest reading the 'One and two-sided testing, mixture distributions' subsection of the documentation (https://go.documentation.sas.com/doc/en/pgmsascdc/9.4_3.4/statug/statug_glimmix_details29.htm ). In the third paragraph, there is a discussion about hypothesis testing when the null value of the parameter is on the boundary of the parameter space. In your case, when you test the null hypothesis that the variance of the random intercepts is zero, you are testing a null hypothesis about a parameter on the boundary of the parameter space (i.e., variance must be greater than or equal to zero). As detailed in the linked subsection, there has been a lot of research into the behavior of the likelihood ratio test statistic under those conditions, such that the likelihood ratio test implemented in PROC GLIMMIX will often provide an asymptotically more powerful and reliable test than the Wald test. For more details, read the papers cited in the documentation.
... View more