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Hello,
I am wondering if someone with familiarity about mixed linear models and non
positive definite matrices as an error message can help me. I'm running a
mixed linear model with 362 individuals nested within 31 cases. The final
model I need to test contains 10 predictors. The only fixed effect I am
specifying is the intercept--the covariates are all being treated as random
effects.
After testing the unconditional model, I've added one variable at a time and
with some combinations, I run into no problems. But as soon as I add certain
variables, I get non positive definite Hessian matrix warnings. I've read
several sources about potential solutions and I'm unsure how to carry them
out in SPSS. Two things we can rule out: the data are balanced (ran multiple
imputation procedure to replace missing values with imputed ones) and the
covariates are all in a similar metric (average of combined z-scores) so the
variances are similar.
2 methods that seem to be promoted often are changing start values using the
EM algorithm (I couldn't find an option for that in SPSS v.14.0) and the
log-Cholesky decomposition method (with a reference to Pinheiro & Bates,
1996), about which I know nothing.
Is there someone on this list who has a method he/she favors to ensure a
positive definite D matrix? I'm not sure what to do at this point.
Additionally, when adding variables one at a time, about 50% of the time I
run into the following warning:
*Warnings*
* *
Iteration was terminated but convergence has not been achieved. The MIXED
procedure continues despite this warning. Subsequent results produced are
based on the last iteration. Validity of the model fit is uncertain.
Again, if you have suggestions for troubleshooting, beyond increasing the
max number of iterations, I'd appreciate any help you can offer.
Thanks very much,
Katherine McKnight
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