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I'm researching the behaviour of a bird called Brent Goose. I plan to collect data on 100 individuals of geese. My response variable is divided into four categories: feeding, walking, aggression and other. I plan to watch a bird for 5 minutes, and record the total proportion of that 5 mins that is spent feeding, walking, in aggression and doing other. For example, a bird watched for 5 mins might spend a total of 2 mins feeding, 1 min walking, 1 min aggression and 1 min doing other. Predictor variables are all categorical or integers and include: habitat, age and date.

Could someone suggest an appropriate statistical model to analyse these data? In particular, a model that can handle the proportional response variable.

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You are watching each bird for five minutes. You want to estimate the effect of covariates on the composition of birds' time expenditure. Composition data follows a Dirichlet distribution; so you should use Dirichlet regression. A Google search of Dirichlet regression turns up many useful top results.

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You should probably make an assumption of normality for starters and see what the data look like. You've probably heard about analyzing proportion data with logistic regression or other specific proportion data relating to underlying binomial or multinomial systems.

Your data aren't like that. Proportions like yours can be pretty much normally distributed but could take on other distributions as well. You're going to have to examine your actual data and come back here once you get an idea of the kinds of distributions of results you have.

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  • $\begingroup$ I'm not seeing how this data falls into the "proportion is not frequency" class...? if you watch something for N minutes, then everything is going to add up to N. You can't have negative proportions like in that post. $\endgroup$
    – Hong Ooi
    Jul 16 '13 at 18:26
  • $\begingroup$ You're right, they cannot be negative in this case. That example specifically selected where they can be negative. However, it's definitely not binomial data and can potentially have it's own distribution where variability is not directly related the level of proportion (like binomial). The distribution needs to be examined and then questions need to be asked about that. $\endgroup$
    – John
    Jul 16 '13 at 19:55

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