[R-meta] multi-level, multiple timepoint model

[Marianne DEBUE]

Hi everyone, 

I am conducting a meta-analysis in ecology. I am confronted to several dependencies and I am not sure how to write the model. 

I have several studies, each corresponding to a specific study site. 
The studies can concern one or several populations (bird, fish, vegetation, crustacean). 
In each study, I have measures of abundance of the different species seen in the site at different timepoints. 
Species, Populations and Timepoints can be common or different between studies. 
So I have this type of structure : 

			T=0 	T=1 	T=2 
Study 1 	Population 1 	Species 1.1 	x 	x 	x 
		Species 1.2 	x 	x 	x 
		Species 1.3 	x 	x 	x 
	Population 2 	Species 2.1 	x 		x 
		Species 2.2 	x 		x 
		Species 2.3 	x 		x 
Study 2 	Population 1 	Species 1.1 	x 	x 	
		Species 1.4 	x 	x 	
		Species 1.5 	x 	x 	
	Population 3 	Species 3.1 		x 	x 
		Species 3.2 		x 	x 
		Species 3.3 		x 	x 

The effect size is a standardized mean difference between pre- and post-intervention. 
I don't know the correlation between the different timepoints. 

1. I first wrote this model : 


res=rma.mv(ES, V, mods= ~ Species, random = ~Timepoint|ID_study,struct="CAR", data=data) 


But I was wondering if a Species-level is not lacking ? 

The ID_study allows me to take into account the spatial correlation between all the species of a same site but shouldn't the temporal correlation be linked to each species ? 




2. Is the following model a better approach ? Am I not losing the advantage of the "struct="CAR"" argument ? 


res=rma.mv(ES, V, mods= ~ Species, random = ~1|ID_study/Species/Timepoint,data=data) 

coef_test(res,vcov="CR2") #I am using the clubSandwich package as I don't have a high number of studies 




3. And last question: is it better to make a meta-analysis per population or to keep all the population in one meta-analysis ? 








Thank you for you help 


Marianne 




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