## Interpreting Covariance Parameter Estimates

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Occasional Contributor
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# Interpreting Covariance Parameter Estimates

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!

Accepted Solutions
Solution
‎11-12-2015 05:13 PM
Valued Guide
Posts: 684

## Re: Interpreting Covariance Parameter Estimates

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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SAS Super FREQ
Posts: 3,842

## Re: Interpreting Covariance Parameter Estimates

Occasional Contributor
Posts: 7

## Re: Interpreting Covariance Parameter Estimates

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

Valued Guide
Posts: 684

## Re: Interpreting Covariance Parameter Estimates

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.

Valued Guide
Posts: 684

## Re: Interpreting Covariance Parameter Estimates

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

Occasional Contributor
Posts: 7

## Re: Interpreting Covariance Parameter Estimates

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

Solution
‎11-12-2015 05:13 PM
Valued Guide
Posts: 684

## Re: Interpreting Covariance Parameter Estimates

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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