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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.

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up vote 3 down vote accepted

This seems to be an ideal situation for ordinal regression, e.g., proportional odds model or log-log link cumulative probability model (discrete Cox proportional hazards model).

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