How do i get a block diagonal covariance matrix, V, in SAS Proc Mixed or Proc glimmix?

[Lyson]

Hi friends,

I am trying to estimate a linear mixed model for treatments arranged in CRD using SAS using proc mixed or proc glimmix. I have 3 categorical factors A, B and C where factor C is assumed random, and A,B are fixed. My data set looks like this:

The  syntaxes that I am exploring are:

a) PROC GLIMMIX

proc glimmix data=FFRgroup outdesign=XZ;;
class factorA factorB factorC  groupA groupB groupC rep;
model yield= groupA | groupB / ddfm=satterthwaite;
random factorC factorA*factorC  factorB*factorC factorA*factorB*factorC /  V;
lsmeans groupA | groupB   / pdiff cl alpha=0.05 ;
Title "FFR Model";
run;

whch displays the following V matrix,

b) PROC  MIXED:

proc mixed data=FFRgroup ;
class factorA factorB factorC  groupA groupB groupC rep;
model yield= groupA | groupB / ddfm=satterthwaite;
random factorC factorA*factorC  factorB*factorC factorA*factorB*factorC /  V;
lsmeans groupA | groupB   / pdiff cl alpha=0.05 ;
Title "FFR Model";
run;

displays the following V matrix,

What could be the problem with these two approaches not producing the covariance structure that aligns with the model in question (block diagonal)? 

Thank you in advance for your assistance folks.

[jiltao]

If you rewrite your RANDOM statement below --

random factorC factorA*factorC  factorB*factorC factorA*factorB*factorC

to the one that makes the model to be processed by subjects and is more numerically efficient --

random int factorA  factorB factorA*factorB / subject=factorC v;

in both procedures, then you would probably see the V option displaying the first block (for the first level of FACTORC) of the variance covariance matrix. Do the two procedures give you the same output for the V matrix?

Also the values in the output you show from PROC MIXED look unusually large to me. What do you see in the Log from PROC MIXED? It might be a good idea to examine the logs from both procedures first.

Thanks,

Jill

[Lyson]

Hi Jill

Thanks for the response. However, I have run both PROC MIXED and PROC GLIMMIX, but the result hasn't changed. I still get a diagonal matrix with single values, part of which is pasted below:

Kindly clarify on the "Log" issue. I do not understand.

[Mike_N]

When you use the V option of the random statement in either Proc Glimmix or Proc Mixed, the default behavior is to print out the first (single) block from the V matrix, not the whole block diagonal matrix. However, both procedures are still using block diagonal V. Note that blocks are usually defined by using the subject= option within the random statement. See here SAS Help Center: RANDOM Statement and here SAS Help Center: RANDOM Statement for more details about how to use the subject= statement to specify the blocks of V. 

[Lyson]

Hi Mike,

As suggested by Jil, I have used the following code:
proc mixed data=FFRgroup ;
class factorA factorB factorC groupA groupB groupC repA repB repC;
model yield= groupA | groupB / ddfm=satterthwaite;
random int factorA factorB factorA*factorB/subject=factorC v;
lsmeans groupA | groupB / pdiff cl alpha=0.05 ;
Title "FFR Model";
run;

And the results are as follows:

[Lyson]

V still diagonal though,,,,

Fixed effects look good...

[Lyson]

Hi Jil & Mike,

I have created another variable "repA" through "repC" to capture the replications in each treatment cell, e.g., in the first cell I recorded "1, 1, 1, 1, 1" for the five replications in each of the rep variables. Then I had to define the "subject = " statement with  repC, the random variable. Is this in order? the data set, code and output are as shown below:

proc mixed data=FFRgroup ;
class factorA factorB factorC  groupA groupB groupC repA repB repC;
model yield= groupA | groupB / ddfm=satterthwaite;
random int factorA factorB factorA*factorB/subject=repC v; 
lsmeans groupA | groupB   / pdiff cl alpha=0.05 ;
Title "FFR Model";
run;

Looks like the V matrix is still a diagonal matrix by default in PROC mixed, as highlighted by Mike.

[Mike_N]

Your subject effect, FactorC, has one distinct level. All 120 observations have the value 'ra'. The subject= part of your model is not specified correctly. The documentation links above should help get you back on the right track.   

[Lyson]

Hi Mike,

If I put back the original variable names in place of factor A, B and C, the code and output are as follows:

proc mixed data=FFRgroup ;
class Treat Depth Incorp   repA repB repC;
model yield= Treat | Depth / ddfm=satterthwaite;
random  Treat Depth Treat*Depth/subject=Incorp v; 
lsmeans Treat | Depth   / pdiff cl alpha=0.05 ;
Title "FFR Model";
run;

Similar results, but I notice the "G matrix not positive definite" issue. How can I improve these results around this issue, if at all it is another problem?

[Mike_N]

I don't think I completely understand what you mean by the 'original' variable names - but renaming the variables won't fix this issue, if that is your question. You should not ignore the warning about the G matrix and you should likewise take note of all of the zeros in the covariance parameter estimates table. I still suspect your subject effect is misspecified, but I can't tell exactly how without your data. I would suggest first trying to fit a simpler model, such as a random-intercept model. That is 

random int / subject = Incorp v;

Once you get that working, start adding in other random factors. 

[jiltao · Accepted solution]

I agree with @Mike_N.

Your first log shows that the final Hessian is not positive definite.

Later, the Log shows that the G matrix is not positive definite.

Your model is likely to be overspecified. You need to take care of your modeling issue first, before attempting to interpret and compare the output.

Simplifying your model, especially your random effects, might be a good place to start.

Thanks,

Jill

[Lyson]

@jiltao  @Mike_N Thank you so much for the assistance. I finally got the diagonal V matrix in the other models. I will deal with the issue of the G matrix not positive definite by reducing the number of random levels and replications. I highly appreciate your assistance. The following two codes give the same results that I want:

proc glimmix data=RFRgroup outdesign=XZ;; 
class Treat Depth Incorp   ;
model yield=  Depth / ddfm=satterthwaite;
random Treat|Incorp Treat*Depth Depth*Incorp Treat*Depth*Incorp /   V ;
lsmeans  Depth  / pdiff cl alpha=0.05 ;
Title "RFR Model";
run;

proc mixed data=RFRgroup ;
class Treat Depth Incorp   ;
model yield=  Depth / ddfm=satterthwaite;
random  Treat| Incorp Treat*Depth Depth*Incorp Treat*Depth*Incorp/ v; 
lsmeans  Depth   / pdiff cl alpha=0.05 ;
Title "FFR Model";
run;

[SteveDenham]

From experience, I think you may not have enough data to be able to distinguish and correctly estimate your RANDOM effects in these models, which would lead to the G matrix issues. Covariance parameter = 0 means you will get the non-positive definite message in the output. So, except in certain regulatory situations, you should simplify the RANDOM statement. 

SteveDenham