Truncated poisson

Hi! i want to fit a truncated poisson model with volleyball sets for a team as response. As we know the maximum of winning sets for a team is 3 . i want to fit truncated poisson via brms. My ub(upper bound) in syntax will be 3 or 4? When i put it 3, it had divergent transitions but with 4 had no problem in convergence. Also, i saw in manual of stan in chapter truncated data that if we want y<300 then we use as ub in stan code (data and model block) that int<upper=300> and y~poisson(λ) T[,300].

I think you would truncate from 4 upward. But I might not do Poisson in this case. I think ordered categorical might work better. Or model the number of points won / lost and obtain the distribution of sets won as a generated quantity.

Thnx for advice. In this phase i try many type of models ( even if these violate some assumptions) and my next steps is to fit some more practical and rational models. But what do you mean when you refer to fitting with ordered categorical? With which categorical response? Concerning the 2nd version with points won/lost is one of my priorities but it will be complex because it is necessary to exist a 2-point difference in order a set to be finished. Therefore there is a need to model this 2-point difference in points.

Ordinal models are in Stan’s user manual.
51.6. Ordered Logistic Distribution
They should be more accurate than truncated poisson. Truncating a poisson is something “ugly”.