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This question already has an answer here:

What is best statistical model to assess effect of habitat type and year (categorical factors), and plant species percent coverage (%), as independent variables on the dependent variable: insect abundance (count)?

I have zeros in my data and the DV is not normally distributed.

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marked as duplicate by Macro, cardinal, gung, Fomite, Peter Ellis Feb 24 '13 at 10:11

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    $\begingroup$ Can you edit your question to include a sample of your data to make a reproducible example? $\endgroup$ – Ben Feb 23 '13 at 16:48
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    $\begingroup$ possible duplicate of Strategy for deciding appropriate model for count data. Another closely related thread is here. I don't feel the need to link to the dozens of other closely related threads. I'm just a little surprised that two of the most active (and senior) users of this site decided to answer this question that is a) vague, devoid of context and b) overlaps with MANY previous threads. Smh.. $\endgroup$ – Macro Feb 23 '13 at 22:36
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For count dependent variables the usual choices are Poisson or negative binomial regression (usually the latter). If there are excess zeroes, there are various choices such as zero-inflated models and hurdle models.

Why are you using year as a categorical variable?

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I agree with @PeterFlom. What matters primarily to the choice of your model is the nature of your response variable. This means you should almost certainly be using a model based on the Poisson distribution. You should check to see if you have overdispersion, and if so account for that. You mention that you have zeros, but that can be fine, if the lambda parameter (which governs the Poisson distribution) is low, so whether that's a problem depends.

The other side of this is that generally no assumptions are being made about the distribution of your explanatory variables, except that they are fixed and known. For example, there is no problem with the fact that plant coverage is a percentile, you just couldn't use a value outside of the interval $(0,1)$ with your model. Likewise, there is no problem with the fact that habitat is a factor, and, although I also find using year as a categorical variable to be weird, it won't really be a problem, either.

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  • $\begingroup$ Poisson regression with overdispersion is not the same as negative binomial regression .... $\endgroup$ – Macro Feb 23 '13 at 22:21
  • $\begingroup$ I'll change that, @Macro; I was under the impression that it was. $\endgroup$ – gung Feb 23 '13 at 22:23
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    $\begingroup$ @gung I think what Marco alludes to here is that negative binomial is a specific model of over-dispersion - namely assuming that the Poisson parameter is sampled from a Gamma distribution. You could generate over-dispersion by sampling the parameter from other distributions and get a different result. For example in some situations mixing a finite number of Poissons has more rational basis (e.g. flipping between two different fixed rates) $\endgroup$ – Corone Feb 23 '13 at 22:38
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    $\begingroup$ @Corne, I was referring to the "quasi-poisson" model, which is what comes to my mind when I hear about an overdispersed poisson regression model; it's the same as the regular poisson regression model except that the variance is, instead of being contrained to be equal to the mean, is a linear function of the mean.This is in contrast to the negative binomial model, in which the variance is a quadratic function of the mean. See, e.g. here. $\endgroup$ – Macro Feb 23 '13 at 22:47
  • $\begingroup$ @Corone Just putting this here because Macro misspelled your name and I worried you might miss his reply. $\endgroup$ – Glen_b Feb 24 '13 at 1:44

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