I'm new to mixed modelling and i'm confused as to whether its appropriate to use a random effect in an analysis I'm doing. Any advice would be appreciated.
my study is testing how well a newly developed index of mammal abundance can predict the value of an established but more labour intensive index. i've been measuring these indices in multiple forest patches, with multiple plots in each forest patch.
because i'm not directly interested in the effect of forest patches, and because my sample plots are nested within forest patches, ive been using forest patch as a random effect. However, I've got a couple of questions about this:
first, i know that random effects allow you to generalise your results across all possible levels of the random factor, not just the ones you sampled. but it seems to me that to make this kind of inference your levels would have to be randomly sampled? My forest patches were not randomly sampled, so can I still use them as a random effect?
second, Ive read that you can test whether it is necessary to have a random effect by doing eg a likelihood ratio test to compare models with and without the effect. I've done this, and it suggests that the random effect model does not explain the data as well as a fixed effects only model. my issue with this is that my plots are still nested within forest patches, and so presumably not independent. so, can i use this LRT approach to justify excluding the random effect, or do i still need to include it to account for nestedness? and if i do end up removing the random effect, is there a way to verify that plots within forest patches can be considered independent?
Thanks for your help!