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RE: st: mfx after xtnbreg and how to compute predicted Y

From   "Pek-Hooi Soh" <>
To   <>
Subject   RE: st: mfx after xtnbreg and how to compute predicted Y
Date   Wed, 22 Oct 2008 17:21:18 -0700

THANKS Maarten again for the detailed explanation and the coding in Stata,
the recommended readings are great. 

I also refer to Cameron, 1998 (regression analysis of count data), which
includes a discussion on Poisson and Negative Binomial estimations with
interaction terms. 

These readings are not easy for me to comprehend fully though. I believe I
have two practical questions left in this interpretation problem.

For your first response about a3 being the main effect of x3 when x2 has
it's mean value, 
1) Is a3 the estimate I obtain with irr option?
2) Must the estimates for both the single term and the interaction term be
statistically significant in the results? What if one or the other is not,
would the interpretation be different? Or it has no change as long as the
model fit is significant.



-----Original Message-----
[] On Behalf Of Maarten buis
Sent: October-21-08 2:00 AM
Subject: RE: FW: st: mfx after xtnbreg and how to compute predicted Y

--- Pek-Hooi Soh <> wrote:
> Hi Maarten, Thanks so much for your detailed explanations, which help
> me understand stata and the technique of interpreting coefficients in
> nonlinear models with interaction terms. To my limited knowledge, few
> published papers discuss such technique in details, so I really
> appreciate your input.

There are actually a lot of papers on that subject, there just isn't
(yet) a concensus on how best to handle interaction terms in a model
that is non-linear in the parameters. There are at least two issues,
both of which I ignored till now: the first is how best to represent
the interaction term. A good starting point there is (Norton, Wang and
Ai 2004) and the references there in. the second issue is that these
effects are likely to be biased. For this issue I recommend the various
working papers, handouts and references in . However, I would
recommend you will continue to ignore these issues untill you fully
understand how to interpret interaction terms in a linear model. A book
I can absolutely recommend concerning the interpretation of these
models in general is (Long and Freese 2006). It doesn't do to much
about interaction terms though.
> But according to your model x2prime x2primeXx3, you stated a3 as the
> effect of x3, do you mean a4 according to this exp(a1 + a2 x2 + a3 x3
> + a4 x2Xx3 )?

No, the effect of x3 on the linear predictor (ln[count]) is (a3 + a4
x2prime). If x2 has it's average value, then x2prime equals 0. So, the
effect of x3 when x2 has it's mean value is (a3 + a4 0) = a3.
> With regard to your suggestion about finding the change in predicted
> y for a standard deviation change in x3 , I want to try diving x3 by
> its standard deviation, do I do it with x3prime/(s.d. of x3prime) in
> both single and interaction term? 

What I would do is the following:

// create a variable touse that is one when all variables are observed:
gen byte touse = !missing(y, x2, x3) 

// standardize x2 and x3:
sum x2 if touse == 1 
gen zx2 = (x2 - r(mean))/r(sd)
sum x3 if touse == 1
gen zx3 = (x3 - r(mean))/r(sd)

// create the interction term
gen zx2_X_zx3 = zx2 * zx3

Hope this helps,

Long, J. Scott and Jeremy Freese (2006) Regression Models for
Categorical Dependent Variables Using Stata, 2nd Edition, College
Station: Stata Press. 

Norton, Edward C., Hua Wang, Chunrong Ai (2004) Computing interaction
effects and standard errors in logit and probit models, The Stata
Journal, 4(2): 154--167.

Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting address:
Buitenveldertselaan 3 (Metropolitan), room N515

+31 20 5986715

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