# Re: st: Multivariate Poisson - Correlation of Error Terms

 From "Austin Nichols" To statalist@hsphsun2.harvard.edu Subject Re: st: Multivariate Poisson - Correlation of Error Terms Date Wed, 9 Jul 2008 13:40:55 -0400

```U.G. Narloch ---
-nlsur- estimates the equations jointly but -suest- just reestimates
standard errors (not point estimates). I gather from your question
that you want some postestimation tools for -nlsur- that don't
currently exist...

webuse nhanes2, clear
egen c=group(strat psu)
poisson iron black [iw=fin]
est sto p1
est sto p2
suest p1 p2, cl(c)
nlsur (iron=exp({b1}+{b2}*bl)) (lead=exp({b3}+{b4}*bl)) [pw=fin], vce(cl c)

On Tue, Jul 8, 2008 at 10:37 PM, Joseph Coveney <jcoveney@bigplanet.com> wrote:
> U.G. Narloch wrote (excerpted):
>
> I have the following model:
>
> y1 =   X' &bgr;1 + Z1' &ggr;1 + &egr;1
> y2  = X' &bgr;2 + Z2' &ggr;2 + &egr;2
> y3  = X' &bgr;3 + Z3' &ggr;3 + &egr;3
> y4 = X' &bgr;4 + Z4' &ggr;4 + &egr;4.
>
> The dependent variables are count variables and X is a vector of explaining
> variables that is identical in each equation whereas Z includes
> equation-specific variables that differ from equation to equation.
>
> I assume that the four count processes are related to one another, so that
> the disturbance terms should be correlated. To estimate these four
> equations in a multivariate model I follow the approach suggested at:
> http://www.stata.com/statalist/archive/2003-08/msg00226.html
> http://www.stata.com/statalist/archive/2004-09/msg00599.html.
>
> First, I estimate each Poisson regressions separately and second I combine
> these results in a joint model via a Seemingly Unrelated Estimation
> (SUEST). Having done this, I would like to test if the error terms are
> really correlated, so that the count regressions cannot be estimated
> independent from each other.
>
> [snip]
>
> --------------------------------------------------------------------------------
>
> My understanding is that combining the separate equations with -suest- isn't
> really the same as simulatneously fitting them, and so it doesn't seem that
> you could estimate multivariate correlation of error terms with -suest- as
> if for a jointly fit set of equations.
>
> For this, you'd probably have to go the route that Stas Kolenikov suggested
> in the second post that you cite, viz., -gllammm-.
>
> The set of equations looks as if you could recast them and use -gllamm- in
> the manner as for structural equations modeling with count or categorical
> variables.  As I recall, the -gllamm- user manual (www.gllamm.org or the
> U.C. Berkeley website) can help you set things up with this approach.  The
> authors also have a book* that's available from StataCorp's online
> bookstore.
>
> Joseph Coveney
>
> *A. Skrondal & S. Rabe-Hesketh, _Generalized Latent Variable Modeling.
> Multilevel, Longitudinal, and Structural Equation Models_. (Boca Raton,
> Fla.: Chapman & Hall/CRC, 2004).

*
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```