Solved – Can we trust the results of PROC MIXED when the G matrix is not positive definite

mixed modelsas

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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Solved – Equivalent mixed models yielding different results in SAS

By default, SAS uses a very simple method to compute the degrees of freedom; it looks to see if the fixed effect appears in a term in the random effects; if so, it uses that random effect as the degrees of freedom.

In this case, the model with random effects of TUBE and TUBE*POSITION do the right thing as this method can tell that POSITION should use TUBE*POSITION. But the model with POSITION / subject=TUBE cannot. Instead, one should tell it to compute the degrees of freedom using another method, usually the Satterthwaite (satterth) for models with only random effects and the Kenward-Roger method (kr) for models with repeated effects structures.

PROC MIXED DATA=dat ;
CLASS POSITION TUBE ;
MODEL y = POSITION /s ddfm=satterth;
RANDOM POSITION / subject=TUBE type=CS;
RUN;

Solved – using a number of variables (dumthe) in mixed model analysis in R

The answer to your first question, defining $Z$, is straightforward within the nlme() function itself:

random = pdMat(X1+X2+X3...X10 ~ 1)

Part two, Toeplitz $\zeta$, requires a custom solution. For the general remove-one symmetric structure, check out toeplitz(0:10). To understand how to build a custom corStruct, check out the function corAR1 in the source. All the implementations are in C; rolling your own will take some time.

correlation = corToep()  # this is the general idea

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Related Solutions

Solved – Equivalent mixed models yielding different results in SAS

Solved – using a number of variables (dumthe) in mixed model analysis in R

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