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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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    $\begingroup$ Related question $\endgroup$ – Dimitriy V. Masterov Dec 12 '13 at 23:40
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    $\begingroup$ GLMs 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. $\endgroup$ – Glen_b Dec 13 '13 at 0:43
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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/

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