I have a dependent variable, which have 0, 1, 2, or 3 for its value. I asked participants to choose three items and coded 1 if it is in a certain category and 0 otherwise. I add the three binary variables to be my dependent variable. So 3 is the maximum value of the variable.
I know that Poisson regression is used a lot for the count dependent variable and right-censored model for the dependent variable with upper limit. But checking examples available in the Internet, it does not seem appropriate to analyze my data.