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. Also see Category: Linear regression, Category: Logistic regression. Other entries about Poisson regression can be found in the
Poisson regression page at my
old website, StATS.
2010
P.Mean: Power calculations for comparison
of Poisson counts across two groups (created 2010-01-11). Suppose you want to compare Poisson count variables across two groups. How
much data would you need to collect? It's a tricky question and there are
several approaches that you can consider.
Other resources
- Generalized Linear Models.
Description: Peter McCullagh and James Nelder wrote the classic reference
for the generalized linear model. The generalized linear model is indeed very
general, as it includes linear regression, logistic regression, and Poisson
regression models as special cases. This book is for students who want more
mathematical details.
- Modeling Frequency and Count
Data. Description: This books presumes that you are already familar
with the Generalized Linear Model, and proceeds to show you how to apply these
models for a fascinating range of data sets. This book is for students who
want more mathematical details.
- Elhai JD, Calhoun PS, Ford JD. Statistical procedures for analyzing mental
health services data. Psychiatry Research. 2008;160(2):129-136. Available at:
http://www.ncbi.nlm.nih.gov/pubmed/18585790 [Accessed May 19, 2009].
All of the material above this paragraph is licensed under a
Creative Commons Attribution 3.0 United States License. This page was written by
Steve Simon and was last modified on
2010-04-11. The material
below this paragraph links to my
old website, StATS. Although I wrote all of the material
listed below, my ex-employer, Children's Mercy Hospital, has claimed copyright
ownership of this material. The brief excerpts shown here are included under
the fair use provisions of U.S. Copyright laws.
Definitions:
2008
- 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.
2007
- 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.
2006
- 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?"
2005
2004
2003
2002
2001
2000
1999
- 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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