2

The Poisson regression model assumes that $E(y) = Var(y) = \mu$. For my data analysis, do I just simply take the mean of my given $y$ variable and find its variance. If they don't equate, then our Poisson regression model is not adequate for my data. This also implies of overdispersion.

kjetil b halvorsen
  • 63,378
  • 26
  • 142
  • 467
lusicat
  • 681
  • 1
  • 10
  • 20
  • 2
    Arguably, not so. Poisson regression is not at all the same as, or reducible to, fitting a Poisson distribution to your response any more than linear regression is the same as fitting a normal distribution to your response. I'd say the main idea is just $Y = \exp(X\beta)$ without even an assumption that the response is counted. That doesn't rule out other models being better (how could it?) but the Poisson regression model is immensely less restricted than common myth would imply. (Where did you find these statements???) – Nick Cox Dec 09 '16 at 15:48
  • See e.g. http://blog.stata.com/2011/08/22/use-poisson-rather-than-regress-tell-a-friend/ – Nick Cox Dec 09 '16 at 15:49
  • Thank you! I was reading a book by Cameron and Trivedi... – lusicat Dec 09 '16 at 16:47
  • 1
    They have written _several_ books together. For a broader view of Poisson regression see e.g. https://mitpress.mit.edu/books/econometric-analysis-cross-section-and-panel-data – Nick Cox Dec 09 '16 at 16:50
  • https://stats.stackexchange.com/questions/183801/count-data-that-does-not-follow-poisson-distribution/183812#183812 – Glen_b Sep 10 '17 at 10:57

1 Answers1

1

Answered in comments, copied below:

Arguably, not so. Poisson regression is not at all the same as, or reducible to, fitting a Poisson distribution to your response any more than linear regression is the same as fitting a normal distribution to your response. I'd say the main idea is just $\DeclareMathOperator{\E}{\mathbb{E}}\E Y = \exp(X\beta)$ without even an assumption that the response is counted. That doesn't rule out other models being better (how could it?) but the Poisson regression model is immensely less restricted than common myth would imply. Poisson regression also uses the assumption that the variance is proportional to the expectation, not necessarily equal, as in the strict poisson model. (Where did you find these statements???)

Some relevant links: http://blog.stata.com/2011/08/22/use-poisson-rather-than-regress-tell-a-friend/ A book: https://mitpress.mit.edu/books/econometric-analysis-cross-section-and-panel-data

kjetil b halvorsen
  • 63,378
  • 26
  • 142
  • 467