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I am working in ecological research on termites, and last year we conducted a series of behavioral tests to check for intraspecific aggression in some mound-building termite species.

To investigate aggression, we conducted experiments between groups of individuals from different colonies and observed their behavior within a certain time frame. The four possible behaviors were differently scored in order to establish an Aggression index per test for later analysis, which was calculated as such:

$Ai = (NAnntennating*0.1+NHeadbanging*0.2+NThreats*1+NBiting*2)/NTotal$

Now, we would like to link the resulting Ais to a number of factors, both fixed and random, so a mixed effect approach is what we aim for here.

However: choosing the model specifications seems difficult because of how the data presents itself. As long as there were behaviors to observe within any given test, the Ai score is locked between 0.1 and 2. The compiled data from all tests (N=184) is heavily left-skewed, with a high density at 0.1 As far as I understand, you would usually want to use certain methods for modeling on certain datatypes, e.g Poisson on count-data, binomial on dichotomous data, and so on. But, based on the process of data collection, how would you define and choose an appropriate approach here? Some papers seem to suggest that this type of data could fall into the specification of "proportional data" since the weighted counts are divided by a changing denominator and locked within an interval, which would mean that a beta regression could work. However, something in my head keeps saying gamma, though I am not sure why.

I already applied log transformations in order to try usual linear regression methods, but the data is not approaching normality this way, so this "easy" way out is apparently not so useful here.

Any additional help is very welcome, I am really not sure how to progress right now.

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