I am using a linear mixed model to explain variation in an object's ratings. These ratings are bounded between 0 and 10 [EDIT: see note below], and take only discrete values (example histogram of the raw data below). Note that the distance between values can be thought of as consistent across the scale (unlike in a typical Likert scale) i.e. the difference between 1 and 2 is about the same as that between 8 and 9.
I know that a normal distribution can be a useful enough approximation for discrete data in some cases, but I suspect that I need to use a generalized linear model for this.
What sort of distribution/link function would be appropriate for this type of data?
Edit: I should note that I am using a mixed model with random effects to account for non-independence due to multiple measurements by some individuals. My apologies for not including this detail earlier.
Edit 2: the bounds are not 0 and 10 as I stated above, but 0 and 9.