GLIMMIX choosing the appropriate covariance structure for spatial data

[AXR]

Hello!

I'm conducting a regression using PROC GLIMMIX and I'm unsure which covariance structure I should use. I'm looking at school level data that are nested in cities that are nested in metropolitan areas, but I am currently using fixed effects for the metropolitan areas. My dependent variable is a percentage outcome, so I use the beta distribution with a logit link. I have nearly 17,000 schools and some cities have as many as 400 schools (e.g., New York City). I think because of computational issues I'm having convergence issues. The only way the convergence criterion is satisfied thus far is when I use TYPE=VC. I've also made the ID variables for cities numeric (city_code_numeric), which I think makes the program more efficient. I would appreciate any guidance. 

proc glimmix data=dat1 empirical;
	class metro_area;
	model school_percent = 

		school_var1
		school_var2
		school_var3
		school_var4
		school_var5

		city_var1
		city_var2
		city_var3
		city_var4
		city_var5

		metro_area

		/ dist = beta link = logit solution ddfm=BW ;
	random _residual_/ subject=city_code_numeric type=VC solution;
	ods output ParameterEstimates=parms;
run;	

[StatsMan]

Did TYPE=CS not converge?  That's the next simplest covariance structure you can apply

[AXR]

Unfortunately, TYPE=CS did not converge...

[StatsMan]

Is the convergence history well-behaved?  Is the convergence criteria steadily decreasing or bouncing around?  If the convergence criteria is moving towards convergence, then try adding NLOPTIONS TECH=NRRIDG;  (i don't think that's the default for your analysis and it is a slightly more robust optimization method).  

If the convergence history is bouncing around, then you may need to simplify the fixed effects.  Mixed models work best when starting small and adding factors to the model.  When the model finally does not converge, that could be telling you that model does not do a good job with your data.

[AXR]

Hi again, the NLOPTIONS TECH=NRRIDG statement helped! The regression seems to be converging regardless of the fixed effects when I use TYPE=VC. My full model also converged when I used TYPE=CS. My next question is then, are there more sophisticated covariance structures that I should try? and then, when using the empirical option, to what degree does the choice of covariance structure matter?

Thanks for your help.