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# st: simulating random numbers from zero inflated negative binomial estimates

 From Daniel Hill-McManus To statalist@hsphsun2.harvard.edu Subject st: simulating random numbers from zero inflated negative binomial estimates Date Mon, 14 Nov 2011 16:04:17 +0000

```Hi,
```
I came across this code recently that Paul wrote in response to a query (see below).
```
```
I've also found it useful, thank you. But working through it I cannot understand why the linear predictor p2 is not exponentiated before being used in rgamma(1/alph, alph*p2).
```
I'd be grateful if someone could point out to me why this is.

Dan

On 3/06/2011 2:56 a.m., E. Paul Wileyto wrote:

I'm not sure whether anyone has answered this yet.

```
First, read the help on zinb post-estimation commands. There are many flavors of "predict" listed there. You will need three of them before you start generating random numbers. The first one you will need is:
```
predict p1, pr

```
That will generate a new variable, p1, which will be the predicted probability of an inflated zero. All the work is done for you.
```
The second predicted quantity you will need is:

predict lp, xb

```
That will generate the linear combination of predictor variables weighted by coefficients for the negative binomial part of the model. Finally, you will need:
```
predict alpha, xb eq(#3)

```
which will generate a variable containing the overdispersion parameter for the negative binomial. With those three bits, you can get on to simulating.
```
Here's my script:

zinb cignums drug  week, inf(drug  week)
predict p1 , pr
predict p2 , xb
predict lnalpha , xb eq(#3)
gen alph=exp(lnalpha)
gen xg=rgamma(1/alph, alph*p2)
gen pg=rpoisson(xg)
gen zi=runiform()>p1
gen newcigs=zi*pg

zinb newcigs drug  week, inf(drug  week)

Paul

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