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Re: st: RE: synthetic ZINB


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu, jhilbe@aol.com
Subject   Re: st: RE: synthetic ZINB
Date   Mon, 6 Jun 2011 07:10:24 +0100

Joe and other Statalist members:

Please remember our longstanding request _not_  to post attachments.
Most members of the list will have received these as unintelligible
gibberish.

In this case, the two .do files posted are in fact readable via

http://www.stata.com/statalist/archive/2011-06/msg00184.html

but not via the Harvard archives.

Nick

On Mon, Jun 6, 2011 at 12:55 AM,  <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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