PROC GLIMMIX for binary data underdispersion

[maggieKlein]

I am using PROC GLIMMIX to run a generalized linear mixed model for binary data with logit link function while controlling for observations nested within subjects nested within centers.  We would like to be able to assess the model fit as well as the fit statistics for the conditional distribution.  When the following code is ran we see that the Pearson Chi-Square / DF is 0.71 suggesting under-dispersion.  Many posts I have read say this is the exception rather than the rule and is uncommon - not much is said about what this means for the model or solutions to the problem; any help is greatly appreciated!

proc glimmix data = dataFinal order = data method=quad empirical ;
  class subjectID centerID  sev(ref="1")
	   region(ref="North America") comorNMDflg(ref="0")
	   dailyDiureticsFLg(ref="0") avgICUadmitCollapse 
            icuRTmanageVentFlg(ref="0");
  model CompFlg(event="1") = sev PEEPConv_IR
					region comorNMDFlg 
		                       dailyDiureticsFLg 
				       rptTimeFrom avgICUadmitCollapse 
                                      icuRTmanageVentFlg
                                / dist=binary link=logit OR solution cl ;
  random intercept / subject = subjectID(centerID) ;
run;

There are 4,091 observations from 415 subjects and 70 centers.

[NMB82]

Did you ever find an answer to this? I'm running a very similar model right now and finding a similarly low chi sq/df indicating under-dispersion (.40).