I am trying to select the correct model for analyzing data from a behavioral sciences experiment. The experiment consists of eight trials for each participant, and each experiment generates a score on the interval [0--8] for each participant. Each trial within the experiment can be conceived of as a binomial choice. The ideal model will give a prediction equation for the estimated score, using values for a small number of binary categorical explanatory variables.
I am inclined to assume a Poisson distribution for the response variable, with a log link, or a negative binomial distribution if overdispersion is an issue. However, the true distribution is truncated, since any score above 8 is not possible.
Is such an approach on the right track? Would it be wiser to treat each trial as a separate outcome, then do a binomial regression with a random effect for participant? (I have seen a similar question on this site, but would appreciate any advice beyond what is given there)