[R-meta] Comparing several predictors and responses & most appropriate model

[Alicia Foxx]

Hi James,

Happy new year and thank you so much for your thoughtful response. We're
working with plants but thought bird ecology might be a more tangible
example. Let's say having a longer beak means you get more seeds and have
healthier offspring - then birds with longer beaks can out-compete birds
with shorter beaks and perhaps produce more fledglings (theory re:
equalizing fitness/fitness differences).

I appreciate your notes on the bivariate MA and think we should explore it
further - we'd be grateful for any readings you could point us to as this
doesn't seem like a popular method as others. I think this was our
confusion with the "outcomes" aspect.

Could you say a little bit more about your note re: " I would think one
could investigate the question by using a bivariate meta-analysis where the
bivariate ES would be (fitness ratio, beak length difference) and the
predictor would be separate indicator variables for each variable (i.e., a
dummy for fitness ratio and a dummy for beak length difference) and the
model would include bivariate random effects with an unstructured
covariance matrix."

I also just came across a preprint (Mahon et al. 2021
<https://www.biorxiv.org/content/10.1101/2021.07.21.453226v1>) that gets at
the non-independence issue that may be helpful in our case.


Thank you,


Alicia
________________________________________

*Dr. Alicia Foxx, MS, PhD*

she/her/hers

Research Scientist

The Chicago Botanic Garden & New Roots for Restoration
<http://www.newrootsforrestoration.org/>

Adjunct Professor: Northwestern University
Associate Editor: Ecological Solutions and Evidence
<https://besjournals.onlinelibrary.wiley.com/journal/26888319>

ResearchGate <https://www.researchgate.net/profile/Alicia-Foxx> & Google
Scholar <https://scholar.google.com/citations?user=nlWrL0YAAAAJ&hl=en>

E: afoxx using chicagobotanic.org

_________________________________________

On Thu, Dec 29, 2022 at 2:13 PM James Pustejovsky <jepusto using gmail.com> wrote:

> Hi Alicia,
>
> This seems like a pretty challenging modeling problem, and (speaking
> personally) I'm reluctant to offer guidance because I don't know the
> scientific context of the problem that you're investigating. Could you say
> more about the evolutionary or ecological question that you're aiming to
> investigate with the synthesis? I follow the example you gave in which
> you're trying to understand how beak length relates to species
> fitness---but is there any relevant ecological theory to suggest *how*
> differences in beak length alter fitness when in competition with another
> species?
>
> So with that disclaimer, below are some comments/reactions to your
> questions.
>
> Best,
> James
>
> On Tue, Dec 27, 2022 at 10:35 AM Alicia Foxx <afoxx using u.northwestern.edu>
> wrote:
>
>> Hello Everyone,
>>
>> My coauthor and I are working on a meta-analysis in which we want to know
>> the relationship (direction and magnitude) between a variable (mean
>> difference on the x-axis) and a log response ratio (on the y-axis). As a
>> toy example, we want to know if differences in beak length between bird
>> species predict fitness outcomes across studies. From each study, we
>> collected differences in beak length between species as well as fitness
>> outcomes of birds alone (i.e., not in competition) and in competition.
>>
> <snip>
>
>>    As you can see, each study contributes several log response ratios
>>    (i.e., y effect sizes) and several raw mean differences (i.e.,
>> predictor
>>    effect sizes). We have several questions:
>>       What is the best model to assess an overall relationship between
>>       differences in beak length and fitness across studies?
>>          It seems that a meta-regression would work for this question but
>>          our concern is that this is an inappropriate model given that
>> we’re
>>          comparing one effect size (mean difference) with another (log
>> response
>>          ratio). We investigated bivariate meta-analyses, but the inputs
>> appear to
>>          both be outcomes.
>>
>>
>
> My first thought would be to use a bivariate meta-analysis, as you
> considered. I'm not sure what you mean by "the inputs appear to both be
> outcomes." Could you say more about what you see as the drawback of
> bivariate meta-analysis?
>
> Ignoring the non-independence issue, I would think one could investigate
> the question by using a bivariate meta-analysis where the bivariate ES
> would be (fitness ratio, beak length difference) and the predictor would be
> separate indicator variables for each variable (i.e., a dummy for fitness
> ratio and a dummy for beak length difference) and the model would include
> bivariate random effects with an unstructured covariance matrix. The
> question of how fitness ratio relates to beak length difference could then
> be answered by looking at the *covariance* between the random effects. One
> could even compute the regression of fitness ratio on beak length
> difference by calculating it directly from the random effects variance
> components (i.e., the covariance divided by the variance of the beak length
> random effects). There's surely some formula for the standard error of that
> beta estimate, but one could also just do a bootstrap (resampling studies)
> to get a standard error / confidence interval.
>
>          How do we account for non-independence at the level of comparison
>>          (Species A vs. Species B, and species B vs. species A), and
>> study. We’ve
>>          thought about nested random effects or even mathematical
>> corrections for
>>          the non-independence.
>>          -
>>
>
> This seems pretty tricky, and is where I would be looking for relevant
> evolutionary/ecological theory to guide how to approach the model. It seems
> like you've really got a system with *three* variables instead of just two:
> 1. Beak length differences (B vs A)
> 2. Competitive fitness of species B when in competition with A (relative
> to baseline fitness)
> 3. Competitive fitness of species A when in competition with B (relative
> to baseline fitness)
> So perhaps there would be a way to do a multivariate regression of
> (competitive fitness of B, competitive fitness of A) on beak length
> difference? A tri-variate meta-analysis model, instead of the bivariate
> model I sketched above?
>
> One thing I wonder about is whether variables (2) and (3) are really
> different things. Is competitive fitness of species B when in competition
> with A a distinct variable from competitive fitness of species A when in
> competition with B? Or are those variables different ways of saying the
> same thing? Or maybe it would make sense to look at a ratio-of-ratios, such
> as
>
> [(competitive fitness of species B when in competition with A) / (baseline
> fitness of B)] / [(competitive fitness of species A when in competition
> with B) / (baseline fitness of A)]
>
> which is the same thing as
>
> [(competitive fitness of species B when in competition with A) /
> (competitive fitness of species A when in competition with B)] / [(baseline
> fitness of B) / (baseline fitness of A)]
>
> This ratio-of-ratios seems like it could be interpreted as a measure of
> how the relative fitness of the two species changes when they are put into
> competition compared to their relative fitness in the absence of
> competition. Using the ratio-of-ratios would allow for use of the bivariate
> model as described above.
>

	[[alternative HTML version deleted]]