# Using poisson regression for continuous data?

my question is as follows: Can the poisson distribution be used to analyze continuous data as well as discrete data?

I have a few data sets where response variables are continuous, but resemble a poisson distribution rather than a normal distribution. However, the poisson distribution is a discrete distribution and is usually concerned with numbers or counts.

Thanks

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How do your empirical distributions differ from Gamma variates, then? –  whuber Feb 10 '11 at 15:15
I have used the gamma distribution for these data. If you use the gamma distribution with a log link you get almost the exact same result you get from an over-dispersed poisson model.However, in most of the statistical packages I am familiar with poisson regression is simpler and much more flexible. –  user3136 Feb 10 '11 at 16:50
Wouldn't there be other distributions that are better, e.g. whuber's suggestion of gamma? –  Peter Flom Feb 10 '11 at 22:49

The key assumption of a generalized linear model that's relevant here is the relationship between the variance and mean of the response, given the values of the predictors. When you specify a Poisson distribution, what this implies is that you are assuming the conditional variance is equal to the conditional mean.* The actual shape of the distribution doesn't matter as much: it could be Poisson, or gamma, or normal, or anything else as long as that mean-variance relationship holds.

* You can relax the assumption that the variance equals the mean to one of proportionality, and still usually get good results.

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I think, in addition to your point, even if @user3136 is not willing to make the assumption of mean = variance, he/she can use the quasipoisson family in glm . –  suncoolsu Feb 11 '11 at 3:45
But my problem is why would you want to transform continous data to discrete. It is loosing information essentially. Also when a simple log transform would have worked, why discretize your data? Using glm works, but every result is asymptotics based (which may or may not hold) –  suncoolsu Feb 11 '11 at 3:47