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

From   Maarten buis <[email protected]>
To   [email protected]
Subject   RE: FW: st: mfx after xtnbreg and how to compute predicted Y
Date   Tue, 21 Oct 2008 10:00:20 +0100 (BST)

--- Pek-Hooi Soh <[email protected]> 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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