st: RE: synthetic ZINB

[jhilbe@aol.com]

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
-------------------------------------------------------------------------
-----

Attachment: zinb_syn.do
Description: Binary data