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

 From "Joseph Coveney" To "Statalist" Subject Re: st: Multivariate Poisson - Correlation of Error Terms Date Wed, 9 Jul 2008 11:37:35 +0900

```U.G. Narloch wrote (excerpted):

I have the following model:

y1 =   X’ β1 + Z1’ γ1 + ε1
y2  = X’ β2 + Z2’ γ2 + ε2
y3  = X’ β3 + Z3’ γ3 + ε3
y4 = X’ β4 + Z4’ γ4 + ε4.

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]

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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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```