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PROC MIXED in SAS sometimes estimates a non-positive definite matrix of the random effects. However PROC MIXED nonetheless provides the estimates and the standard errors of the fixed effects in such a case. Can we consider that these estimates and standard errors are correct ?

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You can make valid inferences on the fixed effects as long as the matrix $\mathbf{V}$ is positive definite, where $\mathbf{V}$ is the variance/covariance matrix of the implied marginal model.

Remember to specify the option nobound in the proc mixed statement.

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    $\begingroup$ Thank you, I will check the $V$ matrix. Do you have a reference for your claim ? And why would I specify the nobound option ? $\endgroup$ – Stéphane Laurent Jun 21 '12 at 13:03
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    $\begingroup$ Yes, this is my reference: Linear Mixed Models - A Practical Guide Using Statistical Software (B.West, K.B.Welch and A.T.Galecki) Chapman & Hall/CRC. If the matrix is not positive definite because, for example, one variance is estimated to be negative and you don't specify the nobound option, that variance will be forced to be equal to 0. $\endgroup$ – boscovich Jun 21 '12 at 13:52
  • $\begingroup$ Ok, thanks. But in my example there is no zero estimated variance. $\endgroup$ – Stéphane Laurent Jun 21 '12 at 14:09
  • $\begingroup$ andrea, do I have to use my hands to derive the $V$ matrix or is it possible to get it from SAS ? $\endgroup$ – Stéphane Laurent Jun 21 '12 at 14:46
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    $\begingroup$ Take a look at the option V of the random statement. $\endgroup$ – boscovich Jun 21 '12 at 14:51

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