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st:poisson vs zip vs nbreg vs zinb


From   C Johnson <cjj1@gpu.srv.ualberta.ca>
To   <statalist@hsphsun2.harvard.edu>
Subject   st:poisson vs zip vs nbreg vs zinb
Date   Wed, 13 Nov 2002 11:06:09 -0700 (MST)

Dear Statalisters:

I am attempting to fit a count model and would greatly appreciate guidance
on selecting from POISSON, ZIP, NBREG, and ZINB.

First, let me state that I had a look at Hardin & Hilbe (2001), Long &
Freese (2001) and http://www.stata.com/support/faqs/stat/nbreg.html which
in total answered some, but not all of my questions.

My data appear to suffer from overdispersion and a prevalence of 0
counts.  Here, my count variable is labeled 'total'.

.  summarize total if  independent=="YES" & allkfold==0 & brn0log1==1

    Variable |     Obs        Mean   Std. Dev.       Min        Max
-------------+-----------------------------------------------------
       total |     160        2.15   4.988288          0         54

. tabulate total if  independent=="YES" & allkfold==0 & brn0log1==1

      Total |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |         78       48.75       48.75
          1 |         19       11.88       60.63
          2 |         19       11.88       72.50
          3 |         18       11.25       83.75
          4 |          7        4.38       88.13
          5 |          1        0.63       88.75
          6 |          5        3.13       91.88
          7 |          3        1.88       93.75
          8 |          2        1.25       95.00
          9 |          2        1.25       96.25
         10 |          2        1.25       97.50
         12 |          1        0.63       98.13
         13 |          1        0.63       98.75
         16 |          1        0.63       99.38
         54 |          1        0.63      100.00
------------+-----------------------------------
      Total |        160      100.00

Those summary stats suggested that ZINB would be most appropriate.
However, after fitting the ZINB model a number of the "inflate"
coefficients and SEs are very large, but the Vuong test suggests ZINB over
NBREG.  The faq http://www.stata.com/support/faqs/stat/nbreg.html notes
similar problems with coefficients and SEs, but provides little
explanation.  Both ZIP and NBREG provide results that are much more
well-behaved.  Given my data and the fact that ZINB does not fit well, it
would appear that ZIP is the best choice.

Any suggestions on why the coefficients for the ZINB model exploded?  Any
advice/confirmation for selection of a count model is also appreciated.

Thanks in advance.

Chris

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