Hi there!
A short summary of my data:
I have song recordings of 60 birds (multiple recordings per bird). During the research period, some birds had more than one nest. Now I want to find out whether song complexity variables (e.g. song length) are related with reproductive success variables (e.g. brood size). I first added 'male number' (each of the 60 males had a specific and original number) as a random effect.
However, now I'm doubting wether or not to include 'nest number' also as a random effect as is actually is another grouping variable next to 'male number'.
Is this a correct thought and if so, how to include two random factors in my formula. This is how I included it myself in R, but I just want to be sure it's right:
lmer(Clutch_size~Song_length + (1|Nr_male)+(1|Nr_nest), data=dd)
Hello Melindy Dirks,
When I am not sure if I should include a random factor to a model, I plot the data (if possible). By analysing the plot you should get an idea if a random factor is necessary. Another possibility would be to calculate one model including a random factor and one model without random effects. By compairing the output of both models it can also get an idea if a random factor is necessary. Independently of the plot and the model comparison you have of course ask yourself the question if random effects in your model makes sense in a biological way.
And be aware that there is a difference between a random slope and a random intercept.
I hope this helps!
Best regards Paul
Thank you Paul Griesberger for your quick answer! From a biological point of view I think both male- and nest number should be included as random effects, because all recordings of a male in the period of e.g. nest # 100 have clutch size 3 (because nest 100 had a clutch size of 3):
Nr_male- Nest_nr- Clutch_size- Song_length
1- 100- 3- 5.4
1- 100- 3- 3.4
1- 101- 2- 5.2
1- 102- 3- 4.7
2- 104- 2- 3.8
The song length could be associated with the specific male, but maybe also to the nest he had in the period he was singing. Did the male sing more complex songs and did the female therefore decided to lay 3 eggs instead of 2? A very very general thought, but you understand why I think both Nr_male and Nest_nr should be included as random effects. But still then the question: how can I include two random effects in a formula?
Yes, I think this makes sense, and yes, the formula is correct.
I disagree slightly with Paul's advice to possibly NOT include a random intercept at all, because the data are obviousely not independent, and the random factor is needed to account for the non-independence.
You might also consider to fit a random slope as well (Paul mentioned that). There is no real consens in the field, but some statisticians are of the opinion that it's generally better to include random slopes wherever possible (http://idiom.ucsd.edu/~rlevy/papers/barr-etal-2013-jml.pdf).
Another remark: if the response (e.g. "cluch_size") is a count number, you should consider fitting a generalized LMM, presumably of the negative binomial family:
glmer.nb(...)
(the function is defined in lme4, like lmer)
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