[R] linear mixed model using lmer

Peter Claussen d@kot@judo @end|ng |rom m@c@com
Tue Mar 15 19:00:38 CET 2022

```Well, it is true that when there are only two levels, t-test and F-tests should give identical inferences, I don’t think that’s the problem in this case.
Instead, remember that we can compute variance components from an anova table, if we write out the expected mean squares and solve algebraically. When I run aov on these data, I get

> summary(aov(yield ~ batch,data=daty))
Df Sum Sq Mean Sq F value Pr(>F)
batch        1   1.03   1.035   0.128  0.724
Residuals   22 177.91   8.087

This would imply a negative variance component estimate for batch, since batch MS is smaller than residual MS. Most mixed model packages constrain variance estimates to be non-negative, so you get 0 from lmer.

It doesn’t help that you only have two levels for batch.  I find negative variance estimates happen more frequently when there are few levels of the effect to be estimated.

Cheers,
Peter C

> On Mar 15, 2022, at 12:12 PM, Jixiang Wu <jixiangwu05 using gmail.com> wrote:
>
> There is no difference when running anova or t-test. So you shouldn't
> expect positive variance between batches.
>
> On Fri, Mar 4, 2022 at 7:06 PM array chip via R-help <r-help using r-project.org>
> wrote:
>
>> Thanks Jeff for reminding me that the attachment is removed. I put it in
>> my google drive if anyone wants to test the data (
>> )
>> I'll try the mixed model mailing list as well.
>> John
>>    On Friday, March 4, 2022, 04:56:20 PM PST, Jeff Newmiller <
>> jdnewmil using dcn.davis.ca.us> wrote:
>>
>> a) There is a mailing list for that:
>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>
>> b) Read the Posting Guide, as most attachment types are removed to avoid
>> propagating worms/viruses. (None seen upon receipt of this email.)
>>
>> On March 4, 2022 4:41:57 PM PST, array chip via R-help <
>> r-help using r-project.org> wrote:
>>> Dear all, I have this simple dataset to measure the yeild of a crop
>> collected in 2 batches (attached). when I ran a simple inear mixed model
>> using lmer to estimate within-batch and between-batch variability, the
>> between-batch variability is 0. The run showed that data is singular. Does
>> anyone know why the data is singular and what's the reason for 0
>> variability? is it because the dataset only has 2 batches?
>>>> library(lme4)> lmer(yield~1+(1|batch),daty)
>>> boundary (singular) fit: see ?isSingular
>>> Linear mixed model fit by REML ['lmerMod']
>>> Formula: yield ~ 1 + (1 | batch)
>>>  Data: daty
>>> REML criterion at convergence: 115.6358
>>> Random effects:
>>> Groups   Name        Std.Dev.
>>> batch    (Intercept) 0.000
>>> Residual             2.789
>>> Number of obs: 24, groups:  batch, 2
>>> Fixed Effects:
>>> (Intercept)
>>>     5.788
>>>
>>> Thanks!
>>> John
>> --
>> Sent from my phone. Please excuse my brevity.
>>
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