Estimation of variance components in random- and mixed-effects models

Thank you very much for your responses and references. Sorry that I missed
mentioning a lot of information.

I am using lme4, and the fixed predictors are all numeric. Only having 3
levels of cohorts is indeed the major issue. After removing insignificant
predictors in the 2nd model, the only factor left is temperature: offspring
trait ~ temperature + (1 | cohort/female/clutch), which gives the
convergence warning.

Now I treat cohort as a fixed effect, but when I include both cohort and
temperature as fixed effects (in the 2nd model), a warning appears:
"fixed-effect model matrix is rank deficient so dropping 1 column /
coefficient". When I remove cohort (2nd model), the two models become very
similar and give similar results.
    offspring trait ~ cohort + (1 | female/clutch)
    offspring trait ~ temperature + (1 | female/clutch)
But am I not introducing pseudoreplicates if I do not include cohort as a
factor?

PS. The section "How do I compute a coefficient of determination (R2), or
an analogue, for (G)LMMs?" in the GLMM FAQ also gives me some insight.
However, the links provided there seem to be not working.

Best regards,
Amy Huang

Am Mo., 28. Juni 2021 um 19:32 Uhr schrieb Ben Bolker <bbolker at gmail.com>:

   See also:

https://stats.stackexchange.com/questions/37647/what-is-the-minimum-recommended-number-of-groups-for-a-random-effects-factor

https://www.biorxiv.org/content/10.1101/2021.05.03.442487v2

  (I should these links, and the blog post link, to the GLMM FAQ ...)

On 6/28/21 1:17 PM, Thierry Onkelinx wrote:

Another issue is that you have too few levels to fit "cohort" as a
random effect. I wrote a blogpost on this a few years ago:
https://www.muscardinus.be/2018/09/number-random-effect-levels/
<https://www.muscardinus.be/2018/09/number-random-effect-levels/>

Best regards,

ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE
AND FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx at inbo.be <mailto:thierry.onkelinx at inbo.be>
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be <http://www.inbo.be>

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Op ma 28 jun. 2021 om 16:31 schreef Ben Bolker <bbolker at gmail.com
<mailto:bbolker at gmail.com>>:

        Are you using lme4? (I'm 99% sure you are, but it's good to be
    explicit.)

        Are all of your fixed predictors numeric (rather than
    factor/categorical) ?

        Note that a convergence warning is a *warning*, not an error:

have

    you checked the troubleshooting steps in ?lme4::convergence (in
    particular, scaling and centering your predictor variables might
    help ...)

        cheers
         Ben Bolker


    On 6/28/21 10:17 AM, Amy Huang wrote:

     > Dear all,
     >
     > I am examining maternal effects, and my data have three

hierarchy

    levels:

     > clutches of the same female, females, and cohorts. My

explanatory

    variables

     > are at the female level (female length, age) and at the cohort

level

     > (temperature).
     >
     > I would like to estimate the variance components of each

    hierarchy level

     > (i.e. relative amount of variance at each level) and then to

find

    out which

     > factors (female length, age, temperature) explain most of the

    variance. For

     > these, I have two models:
     >      offspring trait ~ 1 + (1 | cohort/female/clutch)
     >      offspring trait ~ temperature + female length + age + (1 |
     > cohort/female/clutch)
     >
     > The major problem is that I only have 3 cohorts (and so 3

    temperatures).

     >  From the first model I am able to get the information, but from

    the second

     > one there is an error message: "Model failed to converge with 1

    negative

     > eigenvalue: -2.0e+01". The error pops up probably because I have

both

     > temperature (fixed) and cohort (random) included. Is my approach

    correct?

     > And is there a way to fix this error?
     >
     > Thank you so much for your time.
     >
     > Best regards,
     > Amy Huang
     >
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