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# Re: st: Interpretation of Interaction terms in log-lin

 From Lukas Borkowski To statalist@hsphsun2.harvard.edu Subject Re: st: Interpretation of Interaction terms in log-lin Date Tue, 22 May 2012 13:04:32 +0200

Dear David,

thanks for your quick reply. To get a little bit more into details:

I am investigating the effect of emigration rates (x1) on GDP per capita (y) and use balanced two time period panel. My assumption is that the effect of emigration rates is different when looking at different World Bank income classes, so x2 is a dummy that equals 1 for low-income countries and 0 else. I have several different dummies for all the income classes and some other subsamples.

So I want to interpret the effect of emigration rates on GDP per capita for high-income countries, the differences in this effect between low incomce countries and the reference group (high-income countries) and the overall effect of emigration rates on GDP per capita for low-income countries.

What I have done so far is to calculate exp(ß1) to get the effect for high-income countries, exp(ß3) to get the differences between low- and high-income countries and exp(ß1+ß3) to get the overall effect of emigration rates on GDP per capita for low-income countries. I am just interested in the slopes, the intercept is of no value to me!

So is that correct? How would I interpret exp(ß3)? For exp(ß3) = 1,20, is then that the effect is 20% stronger in low-income countries compared to high-income countries?
Is exp(ß1+ß3) the correct way to see the overall effect or should I compute exp(ß1)+exp(ß3) ?

Regards

#
Lukas Borkowski

Am 22.05.2012 um 12:44 schrieb David Hoaglin:

> Dear Lukas,
>
> Please tell us more about what you are trying to do.  The subject line
> starts with "Interpretation."  What do you wish to interpret?
>
> If, for example, you want to interpret the individual coefficients,
> you must take into account that the definition of each regression
> coefficient includes the set of other explanatory variables in the
> model.
>
> Further, the popular (but oversimplified) interpretation that involves
> changing a predictor by 1 unit while holding the other predictors
> constant cannot be used in your model.  Changing x1 by 1 unit must
> also change x1_x2.
>
> It may be helpful to choose a grid of values of x1 and x2, calculate
> the predicted value of y at each point in the grid, and then
> exponentiate those predicted values.
>
> David Hoaglin
>
> On Tue, May 22, 2012 at 6:24 AM, Lukas Borkowski <LukasBork@hotmail.com> wrote:
>> Dear all,
>>
>> my simplified model can be written as y = ß0 + ß1x1 + ß2x2 + ß3x1_x2 with the last expression being an interaction term.
>>
>> However, the dependent variable is in logs and the explanatory variables are not. I now wonder whether I have to add ß2 and ß3 before putting them into the e-function or to exponantiate each coeffecient seperately and then do the addition?
>
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