I have data on the percentage of their 24h day that animals spend doing certain activies.
One response for one animal may look like
30 % spent hunting
30 % spent sleeping
30 % spent eating
10 % spent mating
And then of course we have many covariates. Our interest lies in measuring the effect of these covariates on these percentages.
This is a compositional data set. The data sums to 100 %. It is usually analysed using log-ratios. This is a multi-variate problem.
Question: .... Can it reasonably be analysed as separate univariate regressions?
Each component has a perfectly sensible independent meaning which is not bemuddled by the correlation structure. If an animal's first component has a 30 % response, then that tells us directly that this animal spent 30 % of a 24h day hunting.
Similar, the last component tells us what percentage of a 24hday the animal spent mating. This too makes sense in isolation.
So, can this data set reasonably be studied by applying, say, 4 separate univariate regressions?
What do you say?
