My name is Eva and I am new here.
I am trying to model pairwise similarites values between islands.
I have 15 archipelagos and 2 animal groups. In each archipelago I calculated similarity values (jaccard index-proportion of common species between 2 islands), inter-island distances, area and elevational differences between all pairs of islands. That is if I have 5 islands in a given archipelago I end up with 10 values for each animal group. Furhtermore, each archipelago is either oceanic or landbridge dependent on the geological history of the islands.
I apply a glmm to the data with archipelago as a random factor. In each archipelago the similarity values (as well as inter-island-distance, area and elevational differences) are not independent of each other because each island contributes to N - 1 of them. Values from different archipelagos are not related to each other.
I fitted a glmm (lme4 package in R) as follows:

data.lmer6=glmer(Beta_diversity ~ Taxon+Island+log10(Area+1)+log10(Distance+1)+log10 (Elevation+1)+(1|Archipelago/Island), data=data_mine, family="binomial", weights=c(N))

Beta_diversity is the similarity values
Taxon is the animal group
Island is the type of the archipelago, either oceanic or landbridge
N is the number of common species between 2 islands

I read that a glmm allows for correlation between the observations of the same random factor. Does this mean that my model is valid (as I believe) or do I have to bootstrap the model parameters since there is a lack of independence between some values. Is it even possible to bootstrap a mixed model? I don't have any programming skills.

Perhaps this is basic statistic knowledge but I have not found an answer yet.
If this is the wrong place to post I apologize