# [R-sig-ME] lmer: problem in crossed random effect model with verydifferent variances

Douglas Bates bates at stat.wisc.edu
Wed Jun 17 22:02:14 CEST 2009

```On Wed, Jun 17, 2009 at 2:48 PM, Doran, Harold<HDoran at air.org> wrote:
> Michael

> I'll take a quick stab at this, but there is really no way to know what
> the issue is given that there is no real description of your data.
> First, SAS and lmer use different algorithms for generating parameter
> estimates, so it's no surprise that the world does not line up exactly
> between the two. However, the estimates should be similar.

> Lmer used REML by default. What did you use in SAS, ML or REML

What are the values of the REML criterion (or the deviance, if you
used ML estimates) at convergence?  If they are very close then it is
just a matter of the convergence criterion.  Consider that the
relative variance for the analyst in the SAS fit is less than 0.01.
When you estimate a variance relative to the residual variance as 0.01
it means "essentially zero"

You should read the result from lmer as an estimate of zero.  For some
reason the optimization software doesn't like to converge on the
boundary and often ends up at very small but non-zero values.

>
>> -----Original Message-----
>> From: r-sig-mixed-models-bounces at r-project.org
>> [mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf
>> Of Michael Li
>> Sent: Wednesday, June 17, 2009 3:15 PM
>> To: r-sig-mixed-models at r-project.org
>> Subject: [R-sig-ME] lmer: problem in crossed random effect
>> model with verydifferent variances
>>
>> Hi, I  remember seeing this mentioned somewhere but couldn't find it.
>>
>> I used lmer to fit a simple linear mixed model with two
>> crossed random effects, day and analyst, with no other fixed
>> effects.  So the syntax is something like:
>>
>> lmer (y ~ (1 | day) + (1 | analyst), data = data)
>>
>> I can also fit the same model in PROC MIXED. Most of the time
>> I got the same answers.  But there seems to be a problem with
>> lmer when one of the random effect has a much smaller
>> variance than others.
>>
>> In my case, SAS would give random effect variances of 1552, 599133 and
>> 213814 for analyst, day and residual effects, respectively
>> but lmer gives 2x10^-12, 599050, and 214680.  Basically all
>> parameter estimates are the same (more or less), except that
>> lmer gives very tiny estimate for the random effect of 'analyst'.
>>
>> I probably should have used log-transformed y.  But aside
>> from that, how can I get lmer to give a sensible answer?  Or
>> is SAS giving the right answer?
>>
>> Thanks,
>>
>> Michael
>>
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>
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```