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Category: Poisson regression. Poisson regression is quite simply a regression model that assumes that the outcome variable follows a Poisson distribution. These regression models are commonly used to predict count or rate variables. These pages describe how Poisson regression works and some of the issues associated with these models. Articles are arranged by date with the most recent entries at the top. You can find the theme and closely related categories, definitions, and other resources at the bottom of this page.
Stats: Modeling a declining count variable (June 14, 2008). I've been working on an interesting project that requires Poisson regression. A company sends out a mailing and gets a certain number of telephone calls back on each of the days following. The number of phone calls is typically (but not always) highest on the first day afterwards and declines rapidly on successive days. I wanted to develop a simple Poisson regression model for this data.
Stats: Upcoming topics in Poisson regression (April 24, 2008). I get a lot of questions about Poisson regression. I feel embarrassed when this happens because my pages on this topic are woefully incomplete. Everything on my web pages is incomplete to some extent, of course, but this is an area with the biggest gaps. I have been planning for quite a while to write more about this topic, and here are some of the areas I want to discuss.
Stats: Confidence interval for a rate (October 10, 2007). Dear Professor Mean, How do you calculate a confidence interval for a rate?
Stats: Calculating rates (April 6, 2007). Someone on the MedStats discussion group asked how to calculate a rate of needlestick incidents. The answer is quite simple, but there are a variety of possible responses.
Stats: Confidence intervals for count data (March 22, 2007). If you have data involving counts, you have several options for computing confidence intervals. All of these approaches rely on approximations to the Poisson distribution or to relationships involving the Poisson distribution and other important distributions. I want to summarize some of these approaches.
Stats: Formulas for cumulative Poisson and binomial probabilities (February 19, 2007). I am updating some material about Poisson regression and noticed that some of the tests and confidence intervals rely on a percentile from a Chi-squared distribution or a gamma distribution. In previous work on binomial confidence intervals, I had noticed the use of a beta distribution and an F distribution. It seems odd to apply percentiles from continuous distributions for confidence intervals involving counting, but the formulas do indeed work. There are well known relationships for the cumulative distributions of the Poisson and binomial distributions that lead to these formulas.
Stats: Books that discuss Poisson regression (January 19, 2007). Someone on the MedStats discussion group asked about books discussing Poisson regression. If you want to use Poisson regression, you need an overview of the generalized linear model. The classic reference: Generalized Linear Models. P. McCullagh, J.A. Nelder (1983) London: Chapman and Hall. is quite old, but the book is still worth reading.
Stats: Poisson regression? Maybe not! (March 10, 2006). 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?"
Stats: Guidelines for poisson regression models (September 21, 1999). Dear Professor Mean, I have just received feedback on a manuscript under review in which one reviewer recommended use of Poisson regression. I am not familiar with this technique--when it is appropriate and/or recommended, what assumptions the data must meet, whether the procedure in SAS? SPSS? I would appreciate a reference and/or citation to article(s) in which it has been used. Thanks! -- Denied Denise
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This webpage was written by Steve Simon on 2007-08-13, edited by Steve Simon, and was last modified on 2008-07-14. Send feedback to ssimon at cmh dot edu or click on the email link at the top of the page.