I'm reading a paper and I'm unsure how valid their methodology is, and I'm trying to find some information related to that.
Basically, they're doing a meta-analysis of swallows and PCB exposure. They're using several different log response ratios (for the effect size) that are related to reproductive success (number of nestlings, number of eggs, successful fledglings, etc). They make a GLMM using the log response ratios as the dependent variable, the rest of their GLMM makes sense. But is it valid to use response ratios across multiple studies in this way? I can't find any example of another meta-analysis being performed this way. None of the books that they cited in the paper, or any of the other studies they cited, go into detail about using GLMM and log response ratios to perform a meta-analysis with an information-theoretical approach across multiple studies. They also vaguely mention using a weighting system for the response ratios (they don't go into detail), but none of their citations explain the validity behind this decision within the context of GLMM and model selection; the citations only explain waiting schemes for traditional meta-analyses.
Do you know of any examples of this approach to a meta-analysis, or any books or anything like that? It might be something that is done frequently, but has a special name that I don't know about or something. I don't have a strong math background.