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!
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.
See p 2-3 of Kincaide (2005) "Guidelines for Selecting the Covariance Structure in Mixed Model Analysis".
Thank you - I have been looking at this document, but still don't understand how the SAS output relates to these matrices.
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.
Also, if you showed some code, we might be able to give you some specific suggestions. But you do need this book
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
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.
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