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

[Alicia Foxx]

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.

   -

      Difference (raw mean difference) in beak length:
      -

         A beak length - B beak length
         -

         A beak length - C beak length
         -

         B beak length - A beak length
         -

         C beak length - A beak length
         -

      Fitness outcomes (log response ratio):
      -

         log(mean(A fitness with B)/mean(fitness alone))
         -

         log(mean(A fitness with C)/mean(fitness alone))
         -

         log(mean(B fitness with A)/mean(fitness alone))
         -

         log(mean(C fitness with A)/mean(fitness alone))
         -

   We want to use such comparisons from *many studies* to obtain a general
   relationship between differences in beak length and fitness outcomes.
   -

      Fitness outcomes:
      -

         log(mean(A fitness with B)/mean(fitness alone)) ~ A-B (beak length)
         -

         log(mean(A fitness with C)/mean(fitness alone)) ~ A-C (beak length)
         -

         log(mean(B fitness with A)/mean(fitness alone)) ~ B-A (beak length)
         -

         log(mean(C fitness with A)/mean(fitness alone)) ~ C-A (beak length)
         -

   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.
         -

         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.
         -

   We’d greatly appreciate any advice that can be shared.


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

_________________________________________

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