I am trying to come up with the right structure for my mixed effects model but struggle a bit to understand what I need to do. At the moment, I think I could use Generalizing Estimating Equations, with a nested covariance structure (ID within Group), where the formula would be equal to score ~ group, but I am not sure.
My data looks like the table below (this is a similar example). As you can see, the score distribution is quite skewed to the left, making it difficult for me to choose the right distribution family.
I would appreciate any pointers/help in the right direction. The main goal of this model is to perform a statistical test to determine whether the distributions of all groups are significantly different.
Context: There is a huge data set of spoken sentences with transcriptions. I transcribe the data using an AI model and the scores are the metric obtained for that instance, you can think of an accuracy-like metric. Now there are some attributes (Group) describing these individuals (ID), like age group. I want to know whether the distributions of scores are significantly different. However, one individual can speak multiple sentences and thus occur multiple times within the same group, for example, age group. Thus, the data violates the in-group independence assumption. Moreover, the scores are non-normally distributed but skewed to the left.
