Thanks very much for your thorough remarks!

>
>> I suspect you are not using the same data between HLM and R and  
>> that may be the problem. That is, in R you create a variable called  
>> ses.gmc thinking this is a group mean centered variable. But, HLM  
>> "automagically" does group mean centering for you if you ask it to.
>>
>> When you work in HLM are you using the exact same data file that  
>> you created for your use in R? Or, are you relying on HLM to group  
>> mean center for you? If so, I suspect that is the issue. In fact,  
>> we can see that the difference in your estimates lies in this  
>> variable and this is the variable you manipulate in R, so I suspect  
>> the error may no be a function of estimation differences, but of  
>> data differences.
>


I followed your suggestion about the possibly different centering  
approach in HLM and did a run only with raw variables (no centering).  
The small differences stay.

> I would check two things: does HLM estimate two variances and a
> covariance for the random effects and is it using the REML criterion
> or the ML criterion.

HLM is using the REML criterion; concerning the variances for random  
effects I couldn't dig deep enough till now to answer this question ...

 From a lot of comparisons I have run now, I can conclude the following:
- fixed effects usually are equal up to 3 digits after the decimal point
- random variance components can show small deviations if they are  
very close to zero (and are not siginificant anyway - following the p- 
value reported by HLM, which is usually > 0.50 in these cases).  
However, I am aware of the discussion concerning the appropriateness  
of p-values reported by HLM (see also http://markmail.org/search/?q=lme4+p-value#query 
:lme4%20p-value+page:1+mid:3t4hxxrlh3uvb7kh+state:results).

Maybe I was too nitpicking about these small differences - they only  
seem to appear in coefficients/ variance components that are  
insignificant anyway. But the discussion was definitely productive for  
me, and I think I now can convince my colleagues to use lme4 instead ;-)
Maybe someoner wants to dig deeper into this issue; the data set from  
the HLM program (HS&B data) can be downloaded here for example: http://www.hlm-online.com/datasets/HSBDataset/HSBdata.zip 
.


Thanks,
Felix


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