Negative Binomial - Poisson
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SPSS20 Win7 64bit
This thread refers to the thread: "Poisson - negative binomial" (Dec. 19, 2011). Suppose the random variable is distributed similar to the Poisson distribution, however, the RV has a smaller variance than average (with E (X) = 20 and V (X) = 15). The variance would be smaller than the expected value of lambda, and thus would no longer be exactly Poisson distributed. Such a distribution can be represented using a parameterized negative binomial distribution. How would one calculate in SPSS the parameterized variant of the negative binomial distribution, P (X) <= 5 with E (X) = 20 and V (X) = 15 ? Thank you.
Dr. Frank Gaeth
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Frank, You're describing a situation in which your data are underdispersed (variance < mean). Why are you proprosing use of a negative binomial distribution? Ryan On Thu, Sep 6, 2012 at 12:45 PM, drfg2008 <[hidden email]> wrote: SPSS20 Win7 64bit |
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Ryan,
what distribution would you take instead (and how to compute p<=x with SPSS)? Generally: -> We have an under- and overdistribution problem. -> I got the information that NegBin is also acceptable in this specific case where E(X)/Var(X)=2 Frank
Dr. Frank Gaeth
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Frank, The negative binomial regression model is not intended to handle underdispersion (conditional variance < conditional mean). There are several modeling options to deal with underdispersion at your disposal, one of which is known as the generalized poisson regression model. No time to work out the answer for you, but the first place to begin, of course, is to examine its probability density function.
Ryan On Fri, Sep 7, 2012 at 3:05 AM, drfg2008 <[hidden email]> wrote: Ryan, |
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Frank, After a quick google search, it seems that the Conway-Maxwell Poisson model handles underdispersion very well, perhaps better than the generalized poisson regression I mentioned previously. Here is the link to the wikipedia page describing this distribution:
Ryan On Fri, Sep 7, 2012 at 11:28 AM, R B <[hidden email]> wrote:
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This post was updated on .
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Frank,
I'm fully aware of what you are asking. I never suggested GENLIN (aka GENMOD in SAS) in my last 2 posts. You need to examine the probability density (mass) function of a random variable that can handle underdispersed count data. Ryan On Sep 8, 2012, at 3:37 AM, Manfred <[hidden email]> wrote: > Ryan, > > thank you. But the model fit (generalized linear model) is not so much the > problem. It's, as I wrote, just the simple question of how to compute the > cumulative probability with SPSS when you know E(x) and V(x) in that > specific case: E(x)/V(x) = 2. > > Something like the simple CDF.POISSON(quant,mean). > > (which does not apply here) > > -> > With SAS I would have a solution (Modeling Zero-Inflated Count Data with > Underdispersion and Overdispersion - Paper Paper 372-2008 SAS / SAS > http://www2.sas.com/proceedings) > > Frank > > > > -- > View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Negative-Binomial-Poisson-tp5714962p5714989.html > Sent from the SPSSX Discussion mailing list archive at Nabble.com. > > ===================== > To manage your subscription to SPSSX-L, send a message to > [hidden email] (not to SPSSX-L), with no body text except the > command. To leave the list, send the command > SIGNOFF SPSSX-L > For a list of commands to manage subscriptions, send the command > INFO REFCARD ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
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Frank, Suppose you have a Poisson random variable with a mean of lambda=3, and you are interested in calculating pr(x<5). You could use the probability density function (http://www.itl.nist.gov/div898/handbook/eda/section3/eda366j.htm) to calculate the probabilities of observing x=0, x=1, x=2, x=3, and x=4, and then sum those probabilities to obtain pr(x<5) as follows:
COMPUTE Poisson_pr_0 = (exp(-3) * (3**0)) / 1. COMPUTE Poisson_pr_1 = (exp(-3) * (3**1)) / (1*1). COMPUTE Poisson_pr_2 = (exp(-3) * (3**2)) / (2*1). COMPUTE Poisson_pr_3 = (exp(-3) * (3**3)) / (3*2*1). COMPUTE Poisson_pr_4 = (exp(-3) * (3**4)) / (4*3*2*1). COMPUTE Poisson_pr_less_than_5_a = Poisson_pr_0 + Poisson_pr_1 + Poisson_pr_2 + Poisson_pr_3 + Poisson_pr_4. EXECUTE. There is no need to use the COMPUTE statements above because SPSS provides CDF.Poisson:
COMPUTE Poisson_pr_less_than_5_b = CDF.POISSON(4,3). EXECUTE. Nevertheless, I've provided the COMPUTE statements based on the PDF to help clarify my point.
Ryan On Sun, Sep 9, 2012 at 7:34 AM, <[hidden email]> wrote: Frank, |
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Also note the useful fact:
P(X)= P(X-1)*Lambda /X . -------
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This post was updated on .
In reply to this post by drfg2008
Thank you Matthew for the mail.
For underdispersion the binomial distribution works perfect. It's much better than Poisson in our case. p = 1-V(x)/lambda n = lambda / [1-V(x)/lambda] then: CDF.BINOM(quant,n,prob) But I'm still in need of a distribution for overdispersion: that is 'Poisson-like' but V(X) > E(X). Am I right that the Neg.Bin. is appropriate for overdispersion of 'Poisson-like' distributions and the SPSS formula CDF.NEGBIN(quant,thresh,prob) can be used as following ? prob= E(x)/V(x) thresh = E(x) * [prob / 1-prob]
Dr. Frank Gaeth
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