StATS: Poisson regression? Maybe not! (created 2006-03-10).

I get a lot of questions about Poisson regression, even though I have very little about it on my web pages. My guess is that there is even less information out there on the rest of the web, so even my meager offerings still place me at the top of the Google search list. I have been wanting to expand my material in this area for quite some time, but just have not had the time.

Anyway, someone asked me today if they could use Poisson regression when their outcome variables was the answer to the question "How many children would you like to have?"

That's an interesting question. One clue that often points me in the direction of the Poisson distribution is a count variable with no obvious upper bound. If there is an obvious upper bound, then a model using a binomial distribution may make more sense. But here, I just have too many misgivings. I suspect that the Poisson distribution would not fit the data well, because the Poisson distribution would exhibit much more variation than I would likely expect for an answer to a question like this.

One quick check would be to compute the mean and variance of the outcome variable. A Poisson random variable would have a variance that is equal to the mean. This is a very crude test, of course.

A good alternative approach might be to use ordinal logistic regression, another model that I'd like to spend some time describing on these web pages.

Related pages:

• Stats: Guidelines for poisson regression models
• Definition: Poisson distribution
• Stats: Sample size for an ordinal outcome (September 22, 2004)

This page was written by Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Poisson regression.