I’m interested in understanding if a count variable (abundance of insects caught in traps) differs between sites (I’ll call this “difference effect”), and assessing if this difference may appear in one area but not another one. My experimental design is:
- 2 areas (categorical: area_1; area_2) - 5 transects (3 in one area and 2 in the other one) (categorical: "A";"B";"C") - 10 sites (2 sites for each transect) (dummy: 0;1) - 80 traps (8 in each site) (counts)
My response variable is sites, and my predictors are groups of insects, each of them a count variable.
I can only compare sites within transects (I cannot compare site 1 in transect A to site 0 in transect B; not sure if this means sites are paired), and, as the areas are distinct from one another, I cannot say the difference effect is the same in both areas, I have to separate this effect somehow.
I’m running logistic regressions in order to know if there is a “difference effect” (a group of insects being more abundant) in one of the sites compared to the other one (within transects and in the same area). It is necessary that transects be integrated as random effects in my models. I can think of two options for modelling this: one option is to run separate analysis for each area, like so:
model_area_1 <- glmer(Sites ~ group1 + group 2 + group3 + group4 + (1|Transect), family = binomial(link = "logit"), data = df_area_1) model_area_2 <- glmer(Sites ~ group1 + group 2 + group3 + group4 + (1|Transect), family = binomial(link = "logit"), data = df_area_2)
The first model has N = 48 and group Transect = 3, while the second one has N = 32 and group Transect = 2.
In the other option, transects would be included as nested within areas in one model:
model_both_areas <- glmer(Sites ~ group1 + group 2 + group3 + group4 + (1|Area/Transect), family = binomial(link = "logit"), data = df_both_areas)
This model has N = 80 and groups Transect/Area = 5 and Area = 2.
I have two questions:
1) is one of the options better than the other? (maybe I should compare them using AIC?). Again, my objective is to understand if a group of insects is more abundant in one site instead of the other, taking into consideration that this might happen in one area, but not in the other.
2) is there any reason for me to use another link function? I saw this answer which says that extensive variables should be dealt with using log link function, so I think this is correct in my models.
Hope this question is pertinent and I have been clear.