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Re: FE: st: Interaction effects


From   Lorenzo Ciari <lorenzo.ciari@learlab.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: FE: st: Interaction effects
Date   Mon, 14 Jun 2010 21:33:53 +0200

Thank you very much.
Still, what I think about my model is that COMP has a significantly lower effect for low SIZE (I don't think of a full interaction). So I would like to test whether the effect of COMP is different for low levels of SIZE. What is the best way in your opinion in the context of a discrete dichotomous model?



Il 14/06/2010 21.17, frone@ria.buffalo.edu ha scritto:
--- On Mon, 14/6/10, Lorenzo Ciari wrote:
I am estimating a probit model and my dependent variable is
entry (0-1) in a given market. I estimate the model using
form level data, so for each firm I observe whether it
enters or not a market (I have multiple markets): I want to
test whether entry depends on a given variable (call it
COMP) and see whether the effect of COMP on entry is
particularly strong for firsm with certain characteristics
(suppose the characteristics SIZE).

1)  Question 1: if I want to test the hipothesis that
COMP has no effect for values of SIZE lower that X, can I
create a dummy = 1 for firms with size<X and then
estimate a model with COMP, SIZE (continuous variable) and
the interaction between (COMP) and the dummy?
No.  The variable used to represent SIZE in the cross-product needs to be
the same as that used for the lower order terms.  The cross-product is not
an interaction until the constituent variables are partialled out.  So the
lower order SIZE should be the same as that used to compute the
cross-product.
So you could estimate:

COMP, SIZE (continuous variable) and the interaction between COMP and SIZE
(continuous)

or

COMP, SIZE (dummy) and the interaction between COMP and SIZE (dummy)

But if you have a continuous measure of SIZE, the first approach is
preferable.


Can I
interpret the interaction coefficient as in OLS (I wouldn't
know how to use AI-Norton inteff command within this
framework, as I do not interact SIZE with COMP, but the new
created dummy....
Greene addresses the suggestion by Ai&  Norton and, in contrast to Ai&
Norton, would suggest yes.  Greene argues that hypothesis tests (about
interactions) "are about model coefficients and about the structural
aspects of the model specifications. Partial effects are neither
coefficients nor elements of the specification of the model. They are
implications of the specified and estimated model."  Then the interaction
can be graphically portrayed in a variety of ways, including predicted
probabilities.  A problem I've had with the Ai&  Norton approach is that
they fail to demonstrate how their plots have any useful substantive
interpretation regarding the "form" of an interaction between predictors.
Understanding the form (shape) of the interaction is much more important
than merely knowing whether or not it is significantly different from
zero.  This is also discussed by Greene--see:

http://w4.stern.nyu.edu/economics/docs/workingpapers/2009/Interaction-Terms-in-Nonlinear-Models.pdf



Also take a look at:

http://ideas.repec.org/p/iza/izadps/dp3478.html


Mike Frone

****************************************************************
Michael R. Frone, Ph.D.
Senior Research Scientist
Research Institute on Addictions
State University of New York at Buffalo
1021 Main Street
Buffalo, New York 14203

Office:    716-887-2519
Fax:        716-887-2477
E-mail:     frone@ria.buffalo.edu
Internet: http://www.ria.buffalo.edu/profiles/frone.html
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