# Categorical variable as response in poisson regression

I have data on damages on flowers from different treatments. The damage was originally count data (number of damages per flower) but the person collecting the data categorized the data in four levels - no damage (0) to a high damage level (3).

I know I could use logistic regression to model the odds but I wonder if it is possible to use poisson regression instead and consider the observed level of damage as a count variable?

If possible, would the intepretation of the dichotomized treatment coefficients be the difference in the logs of expected counts of damage levels for treatment compared to baseline while holding the other variables constant in the model?

The weird intepretation makes me think this is not at all possible.

• I don't see how you can consider it a count. It won't have the properties of a count. Do you know how the recoding was done? – Glen_b -Reinstate Monica Aug 9 '14 at 7:43
• No you are absolutely correct, the variable is clearly bounded! Thank you. – Notquitesure Aug 9 '14 at 11:09
• Further, it won't have the variance = mean property that you see with a Poisson, for example. – Glen_b -Reinstate Monica Aug 9 '14 at 11:34
• Altough I guess that could be solved with negbin or quasipoisson? – Notquitesure Aug 9 '14 at 23:49
• Yes -- presuming we're happy about treating ordinal as interval then at least in some cases those should provide reasonable approximations - suitable for estimation of the mean, at least (but not necessarily suitable models for getting a prediction interval from, because of issues like the boundedness). – Glen_b -Reinstate Monica Aug 10 '14 at 0:02

A Poisson random variable can take any integer value from 0 to $\infty$. If you fit a Poisson regression model to your data, you may get fitted values other than 0, 1, 2, 3. For this reason, I would not use a Poisson regression model.