[R-sig-ME] Meta-analysis for heritability using MCMCglmm?

[Jackie Wood]

Hi Jarrod,

We were finally able to dig into the statistical analysis of our
heritability data (as a reminder, we are conducting a meta-analysis
investigating heritability in relation to population size) and of course a
few questions have come up.

You had mentioned examining the residuals for the model. This may seem like
a "beginner" question, how does one extract the residuals from MCMCglmm?
The residuals.mcmcglmm function does not work. Summary plots of the MCMC
parameter estimates appear to be roughly normally distributed, and the
traces seem fine. Is this what you were referring to? We ran an unweighted
analysis (heritability estimates without SEs) in both MCMCglmm and lmer to
see if they give similar results, and they are basically concordant as
well. However, the residual distribution for the models run in lmer
(treating heritability as gaussian) is slightly skewed. These are from an
unweighted analysis, though, as I have also read that lme4 is unsuitable
for conducting formal weighted meta-analyses.

We also had a few questions that we thought would be worth discussing about
some methodological issues relating to incorporating common estimates of
heritability in the literature. Bayesian methodologies have become
increasingly popular to use when estimating trait heritabilities, but
bayesian estimates do not provide typical standard error or variance
estimates, as parent-offspring/ANOVA/REML methods do. Published bayesian
heritability estimates typically only include asymmetric confidence
intervals, and we unsure whether these can be translated into variance
estimates that can be used to weight our meta-analysis. For now, we plan on
performing a weighted meta-analysis using heritability estimates that
provide S.E.s, and an additional unweighted analysis that will include the
bayesian point-estimates we have collected from the literature. We were
wondering if you resolved this issue in your own heritability meta-analysis
and knew of a way to incorporate bayesian estimates (which form a
considerable proportion of the suitable heritability estimates available,
at least in recent history) into a formal weighted meta-analysis.

Additionally, we were wondering about the suitability of DIC to conduct
model selection for our analysis of heritability. I recall reading on this
SIG list that you had mentioned that there were potential issues using DIC
for hierarchical models as well as non-gaussian data. Since we're treating
heritability as gaussian, would it still be appropriate?

Any advise would be much appreciated!


On Thu, Jan 15, 2015 at 3:41 PM, Jackie Wood <jackiewood7 at gmail.com> wrote:

> Hi Jarrod and Ken,
>
> Hope you had a great New Year! Thanks so much for your responses to my
> inquiry. Given that we've been using MCMCglmm all along, we'll probably
> stick with it unless there's a compelling reason to change programs. We'll
> be running the h2 models in the coming days and will specify a Gaussian
> distribution as Jarrod suggested; we have quite a bit of data so hopefully
> the residuals will behave!
>
> The advice is much appreciated as always!
> Jackie
>
> On Fri, Dec 26, 2014 at 1:58 AM, Jarrod Hadfield <j.hadfield at ed.ac.uk>
> wrote:
>
>> Hi Jackie,
>>
>> The data are not binomial they are continuous: a beta distribution is
>> probably most appropriate for continuos observations bounded by 0 and 1.
>> However, although heritabilities are bounded by 0 and 1, heritability
>> estimates are not necessarily so, depending on the method of inference (for
>> example it would be possible to get a negative parent-offspring regression,
>> either by chance or through certain types of maternal effect).
>>
>> We have just finished a meta-analysis of h2 estimates and just treated
>> them as Gaussian. The distribution of the residuals wasn't far off and I
>> think the conclusions are robust to the distributional assumptions. Have
>> you checked your residuals - do they look badly non-normal?
>>
>>
>> Cheers,
>>
>> Jarrod
>>
>>
>>
>>
>>
>> Quoting Ken Beath <ken.beath at mq.edu.au> on Wed, 24 Dec 2014 12:30:03
>> +1100:
>>
>>  If you have the original data giving the numerator and denominator for
>>> the
>>> proportion then it is binomial data, and can be modelled in a
>>> met-analysis.
>>> I don't know if this can be done with MCMCglmm but should be possible
>>> with
>>> STAN, JAGS or BUGS. All will require a bit of effort in setting up the
>>> model.
>>>
>>> On 24 December 2014 at 07:17, Jackie Wood <jackiewood7 at gmail.com> wrote:
>>>
>>>  Dear R-users,
>>>>
>>>> I am attempting to conduct a meta-analysis to investigate the
>>>> relationship
>>>> of narrow-sense heritability with population size. In previous work, I
>>>> have
>>>> used MCMCglmm to conduct a formal meta-analysis which allowed me to
>>>> account
>>>> for the effect of sampling error through the argument "mev". This was
>>>> relatively easy to do for a continuous response variable, however,
>>>> heritability is presented as a proportion and is therefore bounded by 0
>>>> and
>>>> 1 which clearly changes the situation.
>>>>
>>>> In fact, I am not actually certain if it possible to conduct a formal
>>>> weighted meta-analysis on the heritability data using MCMCglmm. I have
>>>> seen
>>>> elsewhere where data presented as a proportion (survival,
>>>> yolk-conversion
>>>> efficiency for example) has been logit transformed and fitted using a
>>>> Gaussian error distribution (though this was done using REML rather than
>>>> Bayesian modelling) but I don't know if this is a legitimate strategy
>>>> for a
>>>> formal meta-analysis using heritability as a response variable since any
>>>> transformation applied to the heritability data would also need to be
>>>> applied to the standard errors?
>>>>
>>>> I would greatly appreciate any advice on this matter!
>>>>
>>>> Cheers,
>>>> Jackie
>>>>
>>>> --
>>>> Jacquelyn L.A. Wood, PhD.
>>>> Biology Department
>>>> Concordia University
>>>> 7141 Sherbrooke St. West
>>>> Montreal, QC
>>>> H4B 1R6
>>>> Phone: (514) 293-7255
>>>>
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>>>>
>>>> _______________________________________________
>>>> R-sig-mixed-models at r-project.org mailing list
>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>>
>>>>
>>>
>>>
>>> --
>>>
>>> *Ken Beath*
>>> Lecturer
>>> Statistics Department
>>> MACQUARIE UNIVERSITY NSW 2109, Australia
>>>
>>> Phone: +61 (0)2 9850 8516
>>>
>>> Building E4A, room 526
>>> http://stat.mq.edu.au/our_staff/staff_-_alphabetical/staff/beath,_ken/
>>>
>>> CRICOS Provider No 00002J
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>>>
>>> _______________________________________________
>>> R-sig-mixed-models at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>
>>>
>>>
>>
>>
>> --
>> The University of Edinburgh is a charitable body, registered in
>> Scotland, with registration number SC005336.
>>
>>
>>
>
>
> --
> Jacquelyn L.A. Wood, PhD.
> Biology Department
> Concordia University
> 7141 Sherbrooke St. West
> Montreal, QC
> H4B 1R6
> Phone: (514) 293-7255
>
>


-- 
Jacquelyn L.A. Wood, PhD.
Biology Department
Concordia University
7141 Sherbrooke St. West
Montreal, QC
H4B 1R6
Phone: (514) 293-7255

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