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.

  • $\begingroup$ 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? $\endgroup$ – Glen_b -Reinstate Monica Aug 9 '14 at 7:43
  • $\begingroup$ No you are absolutely correct, the variable is clearly bounded! Thank you. $\endgroup$ – Notquitesure Aug 9 '14 at 11:09
  • $\begingroup$ Further, it won't have the variance = mean property that you see with a Poisson, for example. $\endgroup$ – Glen_b -Reinstate Monica Aug 9 '14 at 11:34
  • $\begingroup$ Altough I guess that could be solved with negbin or quasipoisson? $\endgroup$ – Notquitesure Aug 9 '14 at 23:49
  • $\begingroup$ 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). $\endgroup$ – 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.

  • $\begingroup$ This is exactly what I thought. The idea was originally suggested to me from another fellow, I have also read Agresti (2013) and I am certain that it is not the correct method. I should have read it before asking the question! Thank you very much for taking the time to write your answer, the variable is clearly bounded. $\endgroup$ – Notquitesure Aug 9 '14 at 11:09
  • $\begingroup$ What model would you recommend? The the response is clustered in blocks and I have one nominal predictor. $\endgroup$ – Notquitesure Aug 11 '14 at 7:45
  • $\begingroup$ With only one predictor variable, I would do a simple multinomial regression. You can do this with the glm function in R with setting the family option equal to "multinomial". $\endgroup$ – TrynnaDoStat Aug 11 '14 at 13:16
  • $\begingroup$ Even with the clustering? $\endgroup$ – Notquitesure Aug 11 '14 at 13:40
  • $\begingroup$ If I'm understanding correctly, you don't know the clustering rule. So you are limited to modelling the categories. $\endgroup$ – TrynnaDoStat Aug 11 '14 at 13:58

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