Proc Glimmix categorical by categorical interaction (Non-est)

[Ahinoa]

Hello all,

Once more, I come to this community for your help with SAS. I am using Proc Glimmix to fit a mixed-effects logistic regression with random intercept. All the variables I am working with are either binary or categorical. Because I am particularly interested in the effect of one particular variable as a moderator, I am including four interaction terms of level-2 variables in my model.

I have been able to successfully fit the empty, level-2 variables only, and level-2 + level-1 variables models. However, when I run the model with the interaction terms, the output that I get for the solutions for fixed effects as well as the LSMEANS output are missing estimates (Non-est) for both cross-level and  level-2 interaction terms. What surprises me is that I do not get any errors on the SAS log, so I do not have anything to guide me about what might be wrong. 

I am assuming that this is a simple mistake and that because I am a relatively new SAS user, I am just missing what might be wrong. I will really appreciate any advice you might have about strategies that I can use to solve this issue. 

I am attaching the code, and selected output for your reference. 

Thank you!!!

TITLE "MODEL 6 - FIXED EFFECTS RANDOM INTERCEPT MODERATION ANALYSIS ";
PROC GLIMMIX DATA = DISS3.LLCP2017_STRATIFIED METHOD = QUAD (Qpoints = 1) EMPIRICAL = CLASSICAL PLOTS = ODDSRATIO; /* EMPIRICAL = CLASSICAL ->SANDWICH VARIANCE ESTIMATOR*/ 
WHERE ((_RACEGR3 = 5) AND (_RFHYPE5 = 2)); 
CLASS 			/*STATE LEVEL VARIABLES*/
			 	_STATE M_EXPANSION (REF = "No Expansion") GINI (REF = "Low ") SPP_SPECTRUM (REF = "Con") 
				LPERCENTAGE2017 (REF = "Low Composition") PLACE_3 (REF = "Old")

				/*INDIVIDUAL LEVEL VARIABLES*/
				Risk_Profile (REF = "Low Risk") HC (REF = "Low Access") FPL (REF = "Below FPL") _EDUCAG (REF = "Did not graduate high school")
		
				/*DEMOGRAPHIC CHARACTERISTICS*/
				SEX (REF = "Male") _AGEG5YR (REF = "Late Middle Age") MARITAL (REF = "Never Married") RENTHOM1 (REF = "Rent") 
				EMPLOY1 (REF = "Employed") GENHLTH (REF = "Good, Fair, and Poor");

MODEL BPMEDS (DESCENDING) = RISK_PROFILE HC FPL*PLACE_3 _EDUCAG*PLACE_3 SEX _AGEG5YR MARITAL RENTHOM1 EMPLOY1 GENHLTH 
							M_EXPANSION GINI SPP_SPECTRUM LPERCENTAGE2017 PLACE_3 M_EXPANSION*PLACE_3 GINI*PLACE_3 SPP_SPECTRUM*PLACE_3 LPERCENTAGE2017*PLACE_3/ 
							LINK = LOGIT DIST = BINARY SOLUTION DDFM = BW OBSWEIGHT =AW CL ODDSRATIO; /*OBSWEIGHT -> WEIGHT FOR LEVEL-ONE VARIABLES "OBSERVATIONAL LEVEL*/
RANDOM INTERCEPT/ SUBJECT = _STATE TYPE = CHOL SOLUTION; 
COVTEST "CLASS VARIANCE" GLM; 
ODS OUTPUT SOLUTIONR = CLASSEFFECTS_6A;
ODS OUTPUT PARAMETERESTIMATES =PAREST_6A;

/*CROSS-LEVEL INTERACTIONS*/
LSMEANS _EDUCAG*PLACE_3 /ILINK ODDSRATIO /*DIFF = ALL*/ CL; 
LSMEANS FPL*PLACE_3 /ILINK ODDSRATIO /*DIFF = ALL*/ CL; 

/*LEVEL-TWO INTERACTIONS*/
LSMEANS M_EXPANSION*PLACE_3 /ILINK ODDSRATIO /*DIFF = ALL*/ CL ;
LSMEANS SPP_SPECTRUM*PLACE_3 /ILINK ODDSRATIO /*DIFF = ALL*/ CL ;
LSMEANS LPERCENTAGE2017*PLACE_3 /ILINK ODDSRATIO /*DIFF = ALL*/ CL ;

FORMAT 			/*STATE LEVEL VARIABLES*/
			 	M_EXPANSION MED. GINI GIN. SPP_SPECTRUM POL. LPERCENTAGE2017 LAT. PLACE_3 PLA. _STATE STA.

				/*INDIVIDUAL LEVEL VARIABLES*/
				Risk_Profile RIS. HC HCA. FPL POV. _EDUCAG EDU.
		
				/*DEMOGRAPHIC CHARACTERISTICS*/
				SEX _SX. _AGEG5YR AGE. MARITAL MAR. RENTHOM1 REN. EMPLOY1 EMP. GENHLTH GHL.;
RUN; 
QUIT; 

[SteveDenham]

IF all of the higher order lsmeans are estimated in your output, then examine them to see which combinations don't show up.  As a result of incomplete data, lower order lsmeans will be non-estimable.  A simple example:

proc glimmix;
class sex treatment;
model response = sex treatment sex*treatment;
lsmeans sex treatment sex*treatment;
run;

Now suppose that one of the treatments was not applied to males.  The sex*treatment output should include all levels of treatment for females, and all but one for males.  Both main effect lsmeans should be non-estimable.  I suspect that with a model as complex as yours that something like this is leading to the Non-est output.  There won't be anything in the log as far as a WARNING or ERROR because this is the expected behavior.

So the question then is how can this be addressed.  One way is to fit a one-way analysis, where the MODEL statement looks like (in this example):

proc glimmix;
class sex treatment;
model response = sex*treatment;
lsmeans sex*treatment/e;
lsmestimate <insert appropriate label> sex*treatment <insert appropriate coefficients>;
run;

In the agricultural sciences this is often referred to as a "means model".  This ability to calculate appropriate lsmeans is one of the best things about the addition of the LSMESTIMATE statement.  Note also that I added /e to the LSMEANS statement.  This is a great help in identifying which of the many values would go into the LSMESTIMATE statement.

SteveDenham