Re: FE: st: Interaction effects

[Lorenzo Ciari <lorenzo.ciari@learlab.com>]

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
>
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