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I'm trying to understand why when conducting a multilevel model analysis the Hessian matrix is not positive definite (using SPSS). The data I'm analyzing are responses from individuals who are grouped into dyads. Dyad is a level 2 grouping variable where 2 individuals comprise a dyad. I have a score on x for each individual.

Looking at the distribution of x it looks ok (x was positively skewed but looks pretty normal after a log transformation). Scores on x are between 0 and 1.1 with a sd of 0.26.

When I examine the null model where I only include a random intercept for dyad predicting x the Hessian matrix is not positive definite. If I take the x values and randomize them across dyads there are no problems with the Hessian matrix. This suggests to me some dependence of x between dyad members but I don't know why this should be a problem.

Any thoughts?

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  • $\begingroup$ theanalysisfactor.com/wacky-hessian-matrix $\endgroup$
    – Alex R.
    Commented Aug 18, 2015 at 5:23
  • $\begingroup$ Thanks Alex R. So the conclusion here should be that the model can't uniquely estimate any variance between dyads so the appropriate thing to is to exclude dyad from the analysis? $\endgroup$
    – james.skink
    Commented Aug 19, 2015 at 4:44

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This will happen when there is no variation between dyads.

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