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Re: st: RE: synthetic ZINB


From   Muhammad Anees <anees@aneconomist.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: synthetic ZINB
Date   Mon, 6 Jun 2011 11:45:25 +0500

Thanks Dr. Joseph Hilbe!

The book  provides extremely useful content for us interested in count
data analysis. I appreciate your work on Negative Binomial Regression
in detail.

Anees

On Mon, Jun 6, 2011 at 11:13 AM, Ari Samaranayaka
<ari.samaranayaka@ipru.otago.ac.nz> wrote:
> Hi Joseph
> Thank you for providing codes and directing us towards a useful book.
> Ari
>
>  On 6/06/2011 11:55 a.m., jhilbe@aol.com wrote:
>>
>> oops. In the zinb_syn.do code I neglected to amend the label just prior to
>> the synthetic zinb model at the end. The hurdle model caption was retained.
>> I am attaching the correct zinb._syn.do program, and a similar program for
>> synthetic ZIP. The code
>> runs OK, it was simply the caption. My apologies.
>>
>> Joseph Hilbe
>>
>>
>>
>> -----Original Message-----
>> From: jhilbe <jhilbe@aol.com>
>> To: statalist <statalist@hsphsun2.harvard.edu>
>> Sent: Sun, Jun 5, 2011 4:31 pm
>> Subject: RE: synthetic ZINB
>>
>> Statalisters:
>>
>> I happened to see a discussion of synthetic ZINB data on the StataList
>> digest today. There is an entirely different way to approach this - one
>> that creates a full synthetic ZINB model.  I wrote about creating
>> synthetic models in the first volume of the 2010 Stata Journal, and
>> discuss them much more fully in my recently published, second edition
>> of "Negative Binomial Regression" (Cambridge University Press, 572
>> pages). The book discusses most every count model in the literature,
>> providing both Stata and R code for examples. Output is given in Stata,
>> except for the final chapter on Bayesian NB models. I also develop a
>> variety of synthetic count models where it is simple to write your
>> chosen synthetic predictors as continuous predictors, as binary, or as
>> multilevel categorical. You may employ as many predictors as you wish,
>>  from an intercept-only model to one with more than 10 predictors if you
>> wish. The user specifes the desired coefficients for all predictors, as
>> well as levels of predictor. For NB models you also declare the value
>> of alpha you wish to model.
>>
>> It was quite simple to convert the synthetic NB2-logit hurdle model I
>> give in the book to a zero-inflated NB model, with a logit binary
>> component. I am attaching it to this message, but provide it below my
>> signature as well, together with a sample run. Note where the
>> coefficient values are defined in the comment above active code, but
>> the actual values are given in the code where indicated.  I made the
>> predictors here be simple normal variates, but more complex structures
>> are described in the book, and in the Stata Journal article.
>>
>> I find synthetic models like this very useful for testing model
>> assumptions.
>>
>> Best,  Joseph Hilbe
>>
>> ZINB_SYN.DO
>> ==================================================
>> * Zero inflated Negative binomial with logit as binary component
>> * Joseph Hilbe  5Jun2011   zinb_syn.do
>> * LOGIT: x1=-.9, x2=-.1, _c=-.2
>> * NB2  : x1=.75, n2=-1.25, _c=2, alpha=.5
>> clear
>> set obs 50000
>> set seed 1000
>> gen x1 = invnorm(runiform())
>> gen x2 = invnorm(runiform())
>> * NEGATIVE BINOMIAL- NB2
>> gen xb = 2 + 0.75*x1 - 1.25*x2
>> gen a = .5
>> gen ia = 1/a
>> gen exb = exp(xb)
>> gen xg = rgamma(ia, a)
>> gen xbg = exb * xg
>> gen nby = rpoisson(xbg)
>> * BERNOULLI
>> gen pi =1/(1+exp(-(.9*x1 + .1*x2+.2)))
>> gen bernoulli = runiform()>pi
>> gen zy = bernoulli*nby
>> rename zy y
>> * NB2-LOGIT HURDLE
>> zinb y x1 x2, inf(x1 x2) nolog
>> =================================
>>
>>
>>
>> Zero-inflated negative binomial regression        Number of obs   =
>> 50000
>>                                                   Nonzero obs     =
>> 19181
>>                                                   Zero obs        =
>> 30819
>>
>> Inflation model = logit                           LR chi2(2)      =
>> 24712.97
>> Log likelihood  = -88361.63                       Prob > chi2     =
>> 0.0000
>>
>> -------------------------------------------------------------------------
>>
>> -----
>>           y |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
>> Interval]
>> -------------+-----------------------------------------------------------
>>
>> -----
>> y            |
>>          x1 |   .7407043   .0066552   111.30   0.000     .7276604
>> .7537483
>>          x2 |  -1.249479   .0067983  -183.79   0.000    -1.262804
>> -1.236155
>>       _cons |   1.996782   .0069297   288.15   0.000       1.9832
>> 2.010364
>> -------------+-----------------------------------------------------------
>>
>> -----
>> inflate      |
>>          x1 |   .9047498   .0141011    64.16   0.000     .8771121
>> .9323875
>>          x2 |    .095477   .0125229     7.62   0.000     .0709326
>> .1200213
>>       _cons |   .2031966   .0121878    16.67   0.000      .179309
>> .2270841
>> -------------+-----------------------------------------------------------
>>
>> -----
>>    /lnalpha |  -.6778044   .0153451   -44.17   0.000    -.7078803
>> -.6477286
>> -------------+-----------------------------------------------------------
>>
>> -----
>>       alpha |   .5077305   .0077912                      .4926874
>> .5232329
>> -------------------------------------------------------------------------
>>
>> -----
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>
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