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

 From "Pek-Hooi Soh" To Subject RE: FW: st: mfx after xtnbreg and how to compute predicted Y Date Mon, 20 Oct 2008 15:47:14 -0700

```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.

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 )?

Similar to your suggestion, in fact I have mean centered both X2 and X3 and
created a new variable (x2-r(mean))*(x3-r(mean)). Mean centred variables are
supposedly easier to interpret in my case, according to Echambadi and Hess
(2007, Marketing Science).

Using your notation, I have the model a1 + a2 x2prime + a3 x3prime + a4
x2primeXx3prime, in this case, is it a4 alone or (a3 + a4) as the marginal
effect of x3?

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?

Cheers,

Pek

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Maarten buis
Sent: October-20-08 11:14 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: FW: st: mfx after xtnbreg and how to compute predicted Y

--- Pek-Hooi Soh <phsoh22@gmail.com> wrote:
> Two follow up questions: 1) to calculate the marginal effect for a
> two-way interaction term. Do I run IRR option and take the IRR
> coefficients to compute the effect, equivalent to (a3 + a4 x2) as
> follow?
>
> Say, E[y | x] = exp(a1 + a2 x2 + a3 x3 + a4 x2Xx3 )
>
> Then the proportionate change in the conditional mean due to a
> one-unit change in x3 equals (a3 + a4 x2).

An interaction effect implies that there is no single effect of x3, but
as many effects as there are values of x2. If you still want to present
a single effect of x3 then you will have to choose to fix the value of
x2 at some value, for instance the mean. The easiest way to do that is
to scale x2 in such a way that it is zero at that value. If you want to
know the effect of x3 when x2 has it's average value then you can
create a new variable x2prime in the following way:

sum x2 if !missing(x3, y)
gen x2prime = x2 - r(mean)
gen x2primeXx3 = x2prime * x3

And include x2prime x2primeXx3 in your model instead of x2 and x2Xx3.
a3 is now the effect of x3 when x2 has it's average value.

> 2)  I need to compute
> Y2(X1 | other_X_at_mean_value)
>     Y1(X1+1std_dev | other_X_at_mean_value)
>     calculate Y2-Y1.
>
> How do I use the options predict to have the values X1 and X1 + 1 std
> dev ?

see -help lincom- and -help adjust-. Alternatively you can devide x1 by
it's standard deviation and you will get with -irr- the incidence ratio
for a standard deviation change in x1.

-- Maarten

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

Buitenveldertselaan 3 (Metropolitan), room N515

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

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