I study fish in a single large river and want to know if fish length differs between 3 large sampling 'sections' of the river. To answer this question, I measured hundreds of fish lengths within five randomly selected and uniquely coded'side-channels' within each section. There is strong reason to suspect that fish within a side-channel may be more similar than those outside (i.e., non-independent). Also, the side-channels were not randomly selected from the same broader 'population' of side-channels -- i.e., those available for random selection within a section may be more similar than those available for selection at other sections. To put it another way, fish from adjacent side-channels may be more similar than those from two distant side-channels. It seems to me that I then have a nested random effect (Side-channels within sections), but this would have me using section as a fixed effect AND random effect... right? I have not encountered this situation in any cite-able literature.
I just want to know the appropriate model structure to test if fish length differs between sections. Using the lmer() function in lme4 (program R), I see two possibilities:
Modeling side-channel as a non-nested random effect:
lmer(length ~ section + (1|side-channel))
vs.
Modeling side-channel as a nested random effect:
lmer(length ~ section + (1|section/side-channel))
Does the second model structure make sense? Why/why not? Which model structure is therefore more appropriate?
