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# Re: st: logit and mfx for randomized experiments

 From Maarten buis To "statalist@hsphsun2.harvard.edu" Subject Re: st: logit and mfx for randomized experiments Date Mon, 2 May 2011 09:35:05 +0100 (BST)

```--- Daniel Schwartz wrote:
> I have run an experiment using a 2x2 between-subjects design. My dependent
> variable (y) is a dummy (1= if the participant bought a product we were
> offering; 0= if she did not buy it). I'm using the following:
>
> xi: logit y x1 x2 i.x1*x2
>
> x1 is a dummy (e.g. 1= product had a green package, 0= blue package)x2 is a
> dummy (e.g. 1= product had discount, 0= no discount)
>
> So, one person could have seen the product in 1 out 4 ways (green and discount,
> blue and discount, green and non-discount, and blue and non-discount).
>
> Is it OK, to get the results using 'mfx' after running the logit
> command? This would mean, that using the mfx coefficients I can interpreter the
> main and interaction effects of my conditions. In my case, the main effect of x1
> was significant, the main effect of x2 was non significant, and the interaction
> was significant.

Unfortunately no, this is where I agree with Edward Norton, Hua Wang, and
Chunrong Ai (2004). The idea of an interaction effect is that you want to know
how the effect of x1 changes when x2 changes (or vice versa), and -mfx- does
not give you that.

> 1. What's the difference of using odd-ratios instead?

Effects are comparisons of (real or counterfactual) groups. You can compare the
outcomes by computing a difference or a ratio. I think that the key difference
between odds ratios and marginal effects is that the former thinks in terms of
ratios while the latter in terms of differences. So the former is relative
with respect to its baseline odds while the latter represents absolute effects.

Both can be meaningful. Sometimes the research question can tell you whether to

prefer one or the other, but often that is not the case. In those cases I would at
least look at both and understand where potential differences come from, and than
decide how you wish to report your results. I gave in my Stata tip (Buis 2010) an
example on how to do both and compare the results.

> What's the most acceptable way to present these results? (mfx, margeff,
> odd-ratios, inteff)

-mfx- and -margeff- are not acceptable, they do not test the hypothesis that you
want to test. As I said above, both odds ratios and -inteff- are acceptable and
often complementary ways of inspecting the consequences of your model.

> 2. Is it OK that the p-values of are smaller after computing the mfx, compared to
> the raw coefficients of the logit regression?

The p-values from -mfx- test a hypothesis that you do not want to test, so
they are not meaningful.

Hope this helps,
Maarten

M.L. Buis (2010) "Stata tip 87: Interpretation of interactions in non-linear models"
The Stata Journal, 10(2): 305-308.

E. C. Norton, H. Wang, and C. Ai (2004) "Computing interaction effects and standard
errors in logit and probit models." The Stata Journal, 4(2): 154-167.

-------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------

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