I am asked to perform a regression on a dependent variable that only takes positive values. Intuitively one can think of Poisson or negative binomial, but unfortunately the response variable that I am dealing with is not a count variable. How can I perform a regression on such response variable? any ideas?
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1[Related question](http://stats.stackexchange.com/questions/38530/how-does-a-poisson-distribution-work-when-modeling-continuous-data-and-does-it-r) – dimitriy Dec 12 '13 at 23:40
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1GLMs can deal with right skew continuous distributions; there's the gamma and the inverse Gaussian - indeed the whole Tweedie family, indexed by $p$, the power in the variance function; these are continuous for $p>1$. There are other alternatives to GLMs of course, but that's where I'd start. – Glen_b Dec 13 '13 at 00:43
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On this information, many distributions could make sense: gamma, lognormal, etc., etc. In general, generalized linear models with various links (logarithm first and foremost) and various families could all apply.
By the way, the usefulness of Poisson is not limited to count variables; this is a common myth. See for example for a brisk introduction to the question http://blog.stata.com/tag/poisson-regression/
Nick Cox
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