Multi-level analysis, mixed-models: problem with convergence

Dear reader of this post,

I'm conducting research where I have 8 mental health care teams and three dependent variables: victimization, discrimination and social functioning. My research question is whether the socioeconomic status (SES) has influence on my three dependent variables.

My supervisor advised a multi-level model for each of my dependent variables. This is not within my comfort level, so bear with me.

So what happened is I fitted three models for the data I have. First, the Type III test of fixed effects does not generate a significant effect for my dependent variables. So does further fitting even make sense? But I keep getting a warning for problems with my "final Hessian matrix" So I'm left with basically just a linear regression.

So my friend who is a statistician (but lives in an other country) told me I have a problem with convergence. He solved this with "generalised Inverse" in SAS, but I can't seem to find such an option in SPSS, is there a solution?

Any tips or advice would be welcome!

Thanks in advance,



No cake for spunky
I would think if it failed to converge then you would get no solution at all although I am not familiar with SPSS (I run SAS). You would get no results, not just no significant ones (indeed the p value would not show up since no solutions were arrived at). Multilevel models commonly don't converge if you have many random effects. Four is about the most you can have according to some authors and have convergence (it looks to me that you only have two a categorical dummy and the intercept although its not clear to me how many dummy variables you are using). You might want to reduce the number of random effects in your model, say start with just the intercept and rerun the results. Then if it converges add more.

Type III test tell you if a categorical variable as a whole had an impact in SAS rather than one of the dummy variables you split this into. I have not heard this applied to the test of fixed effects itself, but SPSS could use different language or tests than I am familiar with. Its possible to have a random effect be significant even if a fixed effect associated with it is not I think. I believe that some would consider reporting the random effect in that case because it shows there was significant differences in results by group, although personally I would not care about that if the variable itself failed to predict what I was interested in (that is if the fixed effects had no importance).

If you don't know multilevel regression you should read up on it before you run any models. I spent several months doing so and I am still working through it. There are several long threads on this topic on the regression and applied statistics forums which might help some. I suggest Hox, J. J. (2002). Multilevel analysis: Techniques and applications. Mahwah, NJ: Lawrence Erlbaum.


Less is more. Stay pure. Stay poor.
I have had the hessian warning before, don't recall the option/ approximation/asymptomatic work around. So perhaps the inverse thing may work, not familiar with SPSs enough to help.

Though, I would recommend reading up on what is causing the warning, sometimes changing convergence criteria can get you to a suspect result set.


No cake for spunky
In SAS if it converges, having just run this, it says "Convergence criteria met" if it converges. I am sure SPSS has something similar.