Hello,
I am analysing a mixed model design and in the SPSS output, I have an error saying:
The final Hessian matrix is not positive definite although all convergence criteria are satisfied. The MIXED procedure continues despite this warning. Validity of subsequent results cannot the ascertained.
And The covariance parameter is redundant. The test statistic and confidence interval cannot be computed. (The intercept covariance parameter is zero).
I saw solutions to deal with this on the web (changing models, changing the estimation parameters, centering predictors) but changing the estimation parameters does not work, centering predictors does not apply (categorical variable). I am left with changing models but as I only have a random intercept model at this point, I assume this would mean getting back to an OLS model and not take into account the nested design.
I am not sure what to do.
Any insight on this matter would be great.
Thank you!
Hello Claire,
Changing models can also mean choosing a different error structure. Residual vs fit plot, and QQ plot of residuals are useful clues to whether a different error structure is needed. Changing models can also mean using a different link (Generalized Linear Mixed Models). For example, if your data are free of zero values, a gamma error with identity link can be useful in 'taming' a few high, but plausible values. In my experience either one of these approaches can sometimes solve the Hessian problem.
A somewhat different approach to the problem is to run the model that runs, but use a randomization routine to evaluate validity.
For a mixed model, constraining the estimates to the appropriate subsections of the data (REML) would be appropriate.
Hope that helps,
David S
Thank you so much for your answer.
Can I trust the residuals from the mixed model to do the residual vs fit plot as I had a hessian matrix error?
If that is the case, is the solution to use GLMM or can I correct for this in another way?
What do you mean by "constraining the estimates to the appropriate subsections" ?
Thank you,
Claire
Hello Claire,
Replies listed by query--
"Can I trust the residuals from the mixed model to do the residual vs fit plot as I had a hessian matrix error? "
DCS> The residual plot is a diagnostic for detecting problems. The residual plots may well be distorted. You can trust that the residuals plots are telling you something, even if they have been distorted.
"If that is the case, is the solution to use GLMM or can I correct for this in another way?
DCS> In my experience changing the error structure (as diagnosed by the residual plots) or changing the link, can sometimes eliminate the Hessian problems. Beyond that I cannot say.
"What do you mean by "constraining the estimates to the appropriate subsections" ? "
This was jargon (my apologies) to provide a short answer in place of more detailed answer . The concept here is to restrict the estimation routines to appropriate sections of the data. For example, constraining the estimates to just the data in one of the random groups in the random factor. This makes sense if the random groups in the random factor differ in variance. Thanks to modern software and high performance routines we can do this (look up REML). This can potential remedy problems in running the model, by producing more appropriate parameter estimates.
"The covariance parameter is redundant. "
DCS> At a guess one of your ratio scale (numerical) explanatory variables is highly (perfectly?) correlated with another explanatory variable. You can do a quick check by obtaining the pairwise correlations among all pairs of all of your explanatory variables.
Yours in getting it right,
David S
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