st: Count data with known upper limit

[Sébastien Fosse <sebastien.fosse@outlook.com>]

Dear Statalisters,
I am trying to analyze count data where the outcome is the sum of 5 dichotomous variables -each of these 5 variables is associated with a specific “Fail/Pass” criterion. Given this upper limit (of 5), such data don´t seem to be “very Poisson-like”.
Alternatively, I have also thought of an ordered logit model with 5 ordered categories (that is, one category for each possible count). However, I am not sure that those categories would have much sense given the sum structure of those outcome data (that is, a given sum outcome may result from various combinations). To possibly solve this issue, I have heard that the homogeneity of those 5 constructed categories may be checked but I am unsure about the way to do such a check.
Any suggestion or references to select the appropriate model (and Stata commands) for those count data with a known upper limit would be very helpful.
Many thanks.
Sébastien 		 	   		  
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