Interpreting Covariance Parameter Estimates

[as00502]

I am comparing Covariance Structures and using; Unstructured, Variance Components, Compound Symmetry, Heterogeneous Compound Symmetry, Toeplitz, Heterogeneous Toeplitz, Autoregressive(1) and Heterogeneous Autoregressive(1).

When running these for analysis, the 'covariance parameter estimates' are given, but I cannot decipher what most of them mean!

Variance Components gives one number listed as time, which I can only assume is the Variance for all?

Heterogeneous Compound Symmetry gives

Individual variances and a 'CSH'? 

Toeplitz gives TOEP(2), TOEP(3), TOEP(4) and a residual.

Heterogeneous Toeplitz gives Variances and TOEP(1), TOEP(2) and TOEP(3)?

I was hoping someone may be able to explain what these parameters are in terms of their position in each Covariance Matrix?

Thank you!

[Rick_SAS]

See p 2-3 of Kincaide (2005) "Guidelines for Selecting the Covariance Structure in Mixed Model Analysis".

[as00502]

Thank you - I have been looking at this document, but still don't understand how the SAS output relates to these matrices.

[lvm]

This requires a lot of explanation. You should get the book SAS for Mixed Models, 2nd edition (2006), by Littell et al. This is absolutely essential.

[lvm]

Also, if you showed some code, we might be able to give you some specific suggestions.  But you do need this book

[as00502]

Yes, I have been looking at this book, it helps with a few of the structures, but not the ones mentioned above. 

This is the code im using:

proc mixed data=work.all;
class group ID time;
model Interleukin=group time group*time time0;
repeated time/subject=ID(group) type=vc;
run;

giving:

Covariance Parameter Estimates

Cov Parm Subject Estimate

time ID(Group) 0.8989

proc mixed data=work.all;
class group ID time;
model Interleukin=group time group*time time0;
repeated time/subject=ID(group) type=csh;
run; 

giving:

Covariance Parameter Estimates
Cov Parm	Subject	Estimate
Var(1)	ID(Group)	1.5798
Var(2)	ID(Group)	1.2841
Var(3)	ID(Group)	0.4446
Var(4)	ID(Group)	0.3113
CSH	ID(Group)	0.09986

proc mixed data=work.all;
class group ID time;
model Interleukin=group time group*time time0;
repeated time/subject=ID(group) type=toep;
run;

giving:

Covariance Parameter Estimates
Cov Parm	Subject	Estimate
TOEP(2)	ID(Group)	0.1454
TOEP(3)	ID(Group)	0.03786
TOEP(4)	ID(Group)	-0.04633
Residual		0.9053

proc mixed data=work.all;
class group ID time;
model Interleukin=group time group*time time0;
repeated time/subject=ID(group) type=toeph;
run;

giving:

Covariance Parameter Estimates

CovParm Subject Estimate

Var(1) ID(Group) 1.5813

Var(2) ID(Group) 1.3935

Var(3) ID(Group) 0.4481

Var(4) ID(Group) 0.2919

TOEPH(1) ID(Group) 0.2394

TOEPH(2) ID(Group) 0.07267

TOEPH(3) ID(Group) -0.08388

[lvm · Accepted solution]

To start with, you should add the R and RCORR options to the REPEATED statement. This will show you the estimated variance-covariance matrix (and correlation matrix) for your subject. THis will will help you see how the list of variances and/or covariances translate into a matrix. You should also refer to table 15 (9.3 user's guide: "Covariance Structure Examples") in the MIXED chapter to see the various matrices symbolically. Note: your first use of type=vc is just giving a residual (no covariance). The user's guide table gives a toep(2) as an example: you can expand to 3 or 4 using the concept shown in the table.