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Re: st: Poisson Regression


From   Maarten buis <maartenbuis@yahoo.co.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Poisson Regression
Date   Mon, 14 Feb 2011 09:20:23 +0000 (GMT)

--- On Sun, 13/2/11, Alexandra Boing wrote:
> I would like to know how to proceed and the justication
> Mathematical and Statistical. My dependent variable is
> spent on health (0=No   1=Yes). The prevalence was higher
> than 10 percent. Can I do Poisson regression? According
> to this paper published in BMC on line in 2003, registred
> PMC521200 I can do Poisson regression with variable (0=No 
> 1=Yes) and with prevalence higher than 10 percent, but
> other authors report that only I can do Poisson regression
> with the dependent variable= discrete variable and
> prevalence under 10 percent. Which is correct? And what is
> the explanation Mathematical and Statistical?

I agree with Carlo that you need to give a more complete
reference to the article you just refered to.

The -poisson- model for binary variables is used when one
wants to interpret coeficients as risk ratios. The problem
is that when the prevalence is high, the predicted risks 
can easily become higher than 1. Even if the predicted risk
remain less than 1, but are still high, the relationship 
between a continuous explanatory variable and your outcome
variable can have a shape that is just too unrealistic. The
10 percent strikes me as a reasonable "rule of thumb", but 
there is no such thing as a "correct rule of thumb", they 
are always approximate.

I would use -adjust- to get adjusted predictions, and set
the other covariates at such values that the predicted
probability will be as high as possible and plot the 
resulting curves. If the curve still look reasonable, then
there is probably no problem. It may also help to plot the 
curve from a -logit- regression, which would be the obvious
alternative when -poisson- leads to unrealistic 
predictions.

*--------------------- begin example -------------------------
sysuse nlsw88, clear
gen byte highocc = occupation < 3 if !missing(occupation)
gen byte black = race == 2 if race <=2

poisson union south grade highocc black 
adjust south=1 highocc=0 black=1, by(grade) exp gen(pr_poiss)

logit union south grade highocc black 
adjust south=1 highocc=0 black=1, by(grade) pr gen(pr_logit)

twoway line pr* grade, sort            ///
       ytitle("predicted probability") ///
       legend(order( 1 "poisson"       ///
                     2 "logit" ))
*---------------------- end example ---------------------------
(For more on examples I sent to the Statalist see: 
http://www.maartenbuis.nl/example_faq )

Hope this helps,
Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------


      

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