# How to model qualitative body condition scores? Ordinal logistic regression?

I am after some advice on how to model qualitative animal body condition scores?

My overarching research question relates to comparing the body condition of animals across seasons, locations, age groups and sexes.

Many veterinarians and ecologists assign animals a body condition score, to represent the animal's overall condition (usually representing fat coverage in particular). These scores often range from 1-5, in increments of 1 or 0.5, i.e. the values are discrete and bounded. These condition scores are also ordered, 1 being low body condition (emaciated) and 5 being high body condition (obese), with a score of 3 being the optimal body condition score. Furthermore, the difference between two animals with body condition scores of 2 and 3 respectively is not necessarily equivalent to the difference between two animals with body condition scores of 3 and 4 respectively - the scoring is not necessarily evenly spaced due to its subjective nature.

To make things more confusing an animal does not necessarily need to go through lower scores to get to a higher score, rather the way the scoring works, animals generally start at a score of 3 and either move up or down. An example would be an animal that is born with a condition score of 3 and then becomes increasingly emaciated (decreasing to a score of 1 or 2) or increasingly fat (increasing to a score of 4 or 5).

How would such a scoring system be modelled? Assuming the body condition score was the outcome variable.

It has been suggested to me on a previous post that these data follow a beta-binomial distribution (see here), and hence could be modelled using beta-binomial regression. It has also be suggested to me by colleagues offline that these data could be modelled using ordinal logistic regression (some good posts on ordinal logistic regression are here and here). However, I am unsure if beta-binomial is appropriate as my understanding is that this distribution describes the number of successes out of N trials. Equally I was unsure if ordinal logistic regression is appropriate as its interpretation relates to the odds of obtaining a particular score or less, where in this scoring system a score of 3 theoretically has the highest probability, a score of a score of 4 or 2 then have equal probability and a score of 5 or 1 have equal probability. In this scoring system, animals do not progress through the lower scores to achieve a higher score.

A small example dataset from some recent work would be:

set1 <- as.data.frame(c(3,3,2.5,2.5,4.5,3,2,4,3,3.5,3.5,2.5,3,3,3.5,3,,3,4,3.5,3.5,4,3.5,3.5,4,3.5)
colnames(set2) <- "body_condition"