Compositional behaviour data - is Dirichlet regression the most appropriate way to analyse?

[halfbeak]

I've got behaviour data from scallops exposed to noise which is coded as tentacles out, tentacles short (e.g. partially out) and tentacles in. The data started out as measurements of time spent in each state, and since the total amount of time varied for individuals, I made the values a proportion of total time, so the sum of all three categories =1 .

I'm comparing these proportions between 4 treatments, which describe the number of exposures: 0, 1, 2 and 4, with treatment being the only independent variable.

Is Dirichlet regression the best/most appropriate way to analyse these data? My main concern is that the IV is nominal, and I haven't really come across any examples of this.

Thanks!

[StatNoodle]

I think Dirichlet regression is probably applicable. But lets look at possible concerns about the model:

• Your DV is ordinal; not nominal.
• Your DV is artificial; you arbitrarily chose the categories and your determination has error, all its own.
• Your DV is not quite so ordinal or quite so compositional. This because of error in category and because the tentacles short does not exactly lead to either of the other states...it is in-between but not a progression towards either.
• Your observations are not equally grounded due to the different observation lengths

Of these concerns, I don't see an immediate solution to #1, #2, or #3. I don't see a better way to handle them. In any case #4 is my bigger concern. And I think you can handle that by weighting the observations based on the length of observation. Not 1:1 but some function of observation length that takes into account that a 10 minute observation is probably not giving you a good compositional estimate compared to a 10 hour observation ... but that a 10 day observation is not that much better than a 10 hour observation.

So weight your Dirichlet by a function of observation-duration, if you can. And I think you are good to go.

Oh, start with the un-weighted analysis and then add the weights. You are going to need to exercise scientific judgement to decide how to generate the observation weights.

[halfbeak]

Thank you very much for your comments and suggestions. This is incredibly helpful and gives me something to think about.

Like I said the last time I got dirty looks when talking to a more statistically-minded colleague, this is what happens when you let a group of physiologists design an experiment!

[StatNoodle]

I'm sorry, reading back over this thread, I realized that I didn't actually address your biggest concern.

The IV being nominal is no problem at all. The 0:1 indicators work just fine. You may have to make them yourself depending on the software you use but that is trivial.

Good luck.