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11-12-2015 03:31 PM

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!

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Solution

11-12-2015
05:13 PM

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11-12-2015 04:46 PM

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11-12-2015 03:37 PM

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

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11-12-2015 03:40 PM

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

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11-12-2015 03:52 PM

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.

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11-12-2015 03:53 PM

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

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11-12-2015 04:32 PM

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

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11-12-2015 04:46 PM