I have quite a complicated data set to analyze, and I cant find a good solution for it.
Here is the thing:
1. the raw data is essentially insect song recordings. Each song is made of several bursts, and each burst made of sub-units. All individuals have been recorded for 5 minutes. The number of bursts and their position in the recording can be very different between individuals, as well as the number of sub-units per burst.
2. I have the carrier frequency (fundamental frequency) of each sub-unit, and that's what I want to analyze.
1. The frequencies within a burst are not independent obviously (although it's pretty stable, but the frequency of the sub-unit n-1 will have an influence on the sub-unit n).
2. The bursts are also not independent, within a recording.
3. They are even less independent as the frequency drops with time (the individual gets tired of singing so the frequency of the song gets lower and lower). The dropping seems to be linear.
4. Nesting = I have 3 replicated populations for two locations A and B. So I have A1, A2, A3 & B1, B2, B3.
What I would like to do:
1. Characterize the difference in frequency between my two locations (test it statistically)
2. Characterize the frequency dropping between the two locations (see if it drops faster in one of them)
How to do it:
Well that's why I need help: I don't know. It seems that my case combines problems that are usually not seen together. I've read about mixed models, about GAM, about ARIMA, random and fixed effects, but I cant be really sure of the best way to do it. When I graph it though (frequency ~ sub-unit number n), the difference is very clear between the two locations. I also have to take other variables into account, like the temperature (makes the frequency higher), etc.
I thought about:
Nesting the individuals within the replicate their are from, and nest the replicate within the location (individual/replicate/location).
Use a random 'burst' effect, so I take into account the variability within each burst.
Use a fixed 'burst position in recording' effect, to measure the frequency dropping (hoping it is actually linear).
Would it be correct?
Is there a special type of model I could use for this kind of scenario?