[R-sig-ME] zero variance and standard deviation in random effects

[Ben Bolker]

   I agree.  There is more discussion at

http://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#singular-models-random-effect-variances-estimated-as-zero-or-correlations-estimated-as---1

   While I appreciate Carola Bloch's input, I think it's a little 
misguided.  Having only three levels of the random effect is indeed 
problematic, but it doesn't actually violate any assumptions of the 
model, and there isn't necessarily anything else wrong with the model -- 
it's just hard to estimate variance reliably from a sample of three. 
(See https://rpubs.com/bbolker/4187 for some simulated examples.) One 
standard approach to this problem is to treat province as a *fixed* effect.

On 11/2/21 10:57 AM, Viechtbauer, Wolfgang (SP) wrote:
> When the variance is estimated to be zero, then this is identical to removing the random effect altogether. So whether you remove it or not will not make any difference. I would leave it in and just report the results you obtained. One can also use confint() then to obtain a CI for this variance component. While the estimate (and hence lower bound) are 0, the upper bound is likely to indicate that there could be (substantial) variance associated with this random effect.
> 
> Best,
> Wolfgang
> 
>> -----Original Message-----
>> From: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces using r-project.org] On
>> Behalf Of Tahsin Ferdous
>> Sent: Tuesday, 02 November, 2021 14:57
>> To: Carola Bloch; r-sig-mixed-models using r-project.org
>> Subject: Re: [R-sig-ME] zero variance and standard deviation in random effects
>>
>> Thanks a lot. My model is a random intercept model. But from the "coef(m2)"
>> command, I have found the following results:
>>
>> Prov      Intercept
>> AB.       0.07346574
>> MB.      0.07346574
>> SK.       0.07346574
>>
>> That means intercepts are identical for all three provinces. In this model,
>> Prov is the random effect that has three-level (AB, MB and SK). In this
>> case, what should I do? If I remove province, the model will not be then
>> mixed model. But my data is repeated measures. I have also attached the
>> plot by running the command ( performance::check_model()).
>>
>> On Tue, Nov 2, 2021 at 12:11 AM Carola Bloch <carola.bloch using uk-koeln.de>
>> wrote:
>>
>>> Hi,
>>>
>>> thanks for sharing your problem. Concerning your first question, I would
>>> not recommend running a regular regression, as the data points in your
>>> sample are not independent and this would inflate the type 1 error rate.
>>>
>>> In order to find out why the residual variance shows strange values, I
>>> would try some trouble shooting. You could run coef(m2) and check whether
>>> there are actually different intercepts for Prof. Second I would check
>>> the model assumptions, possibly there is a violation of the assumptions
>>> that affects model fit (I'd recommend performance::check_model()).
>>> Furthermore, how many factor levels does Prof have, I assume 3 according
>>> to your output? A small number of levels might be problematic, see
>>> Singman & Kellen, 2019*.
>>>
>>> *Singmann, H., & Kellen, D. (2019). An introduction to mixed models for
>>> experimental psychology. In *New methods in cognitive psychology* (pp.
>>> 4-31). Routledge.
>>>
>>> Hope this helps!
>>> ------------------------------
>>> *Von:* R-sig-mixed-models <r-sig-mixed-models-bounces using r-project.org> im
>>> Auftrag von Tahsin Ferdous <tahsinferdousuofc using gmail.com>
>>> *Gesendet:* Dienstag, 2. November 2021 05:57:26
>>> *An:* r-sig-mixed-models using r-project.org
>>> *Betreff:* [R-sig-ME] zero variance and standard deviation in random
>>> effects
>>>
>>> Hi,
>>>
>>> I am running a mixed model using lmer like this:
>>>
>>> m2<-lmer( logSeverity~  Incidence+Year+ (1|Prov), data = prov1,REML =
>>> FALSE)
>>>
>>> Here, prov is my random effect. But I have the result, where the random
>>> intercept of random effect is zero.
>>>
>>> Random effects:
>>>   Groups   Name        Variance Std.Dev.
>>>   Prov     (Intercept) 0.00000  0.0000
>>>   Residual             0.01149  0.1072
>>> Number of obs: 54, groups:  Prov, 3
>>>
>>> Should I still run a mixed model using Prov as a random effect, or I run
>>> regression model here instead of mixed model by removing "Prov".
>>> My data structure is like this:
>>>
>>>     Prov Year Incidence Severity
>>>    MB 2020 31.5 0.29
>>>    MB 2019 21.8 0.36
>>>    MB 2018 20.4 0.23
>>>    MB 2017 31.1 0.31
>>>    MB 2016 90.1 1.34
>>>    MB 2015 63.4 0.5
>>>    MB 2014 57.5 0.7
>>>    MB 2013 44.1 0.45
>>>    MB 2012 42.9 0.8
>>>    MB 2011 15.6 0.92
>>>    MB 2010 50.9 1.23
>>>    MB 2009 32.1 1.56
>>>    MB 2008 52.4 1.71
>>>    MB 2007 15.1       0.83
>>>    MB 2006 4.3       0.65
>>>    MB 2005 47.7 1.4
>>>    MB 2004 16.4 1.58
>>>    MB 2003 39.3 0.33
>>>    SK 2020 25.7 0.33
>>>    SK 2019 37.3 0.54
>>>    SK 2018 14.2 0.32
>>>    SK 2017 4.8        0.51
>>>    SK 2016 85.2 1.53
>>>    SK 2015 53.2 0.57
>>>    SK 2014 68.1        1.45
>>>    SK 2013 23.2 0.39
>>>    SK 2012 49.8 1.14
>>>    SK 2011 10.6 0.79
>>>    SK 2010 13.5 1.5
>>>    SK 2009 6.9       0.56
>>>    SK 2008 7.6 0.92
>>>    SK 2007 2.4 0.75
>>>    SK 2006 0.7 0.58
>>>    SK 2005 4.1 0.71
>>>    SK 2004 1.7 0.4
>>>    SK 2003 1.9 0.09
>>>    AB 2020 8 0.34
>>>    AB 2019 28.3 0.52
>>>    AB 2018 2.8 0.37
>>>    AB 2017 3.7 0.49
>>>    AB 2016 32.8 0.59
>>>    AB 2015 9.2 0.29
>>>    AB 2014 24.6 0.25
>>>    AB 2013 17.6 0.4
>>>    AB 2012 10.3 0.63
>>>    AB 2011 5.2 0.87
>>>    AB 2010 3.9 1.68
>>>    AB 2009 3.2 1.13
>>>    AB 2008 0.4 0.78
>>>    AB 2007 0.1 0.45
>>>    AB 2006 0.1 0.78
>>>    AB 2005 1.1 1.09
>>>    AB 2004 1.2 0.82
>>>    AB 2003 1.2 0.08
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-- 
Dr. Benjamin Bolker
Professor, Mathematics & Statistics and Biology, McMaster University
Director, School of Computational Science and Engineering
(Acting) Graduate chair, Mathematics & Statistics