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Trying to figure out the most appropriate family for a data type I'm not used to.

For each measurement, I have a bunch of attempts, with the outcomes falling into bins: failure, small, medium or large.

Each attempt must result in one of the above (categories are exclusive and exhaustive). In some ways it seems a simple multinomial problem.

However, details of the system make me worry about treating the categories as independent. The data result from animal foraging attempts and indicate prey size:

  • prey size distribution declines with size: small prey are commoner than medium, than large.
  • catching large prey is harder than catching small ones.

Therefore, intuitively it seems that failure < small < medium < large.

Does it make more sense to treat each attempt as some kind of ordinal regression problem, e.g. adjacent categories? I'm struggling to wrap my head around how each category's probability is related to the others'.

Thanks very much in advance!

(Will be coding this as part of a SEM in brms in R, if anyone has specific suggestions).

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