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# RE: st: Interaction in logit

 From "Mustillo, Sarah A" To "'statalist@hsphsun2.harvard.edu'" Subject RE: st: Interaction in logit Date Wed, 27 Oct 2010 10:04:50 -0400

```Hi Teemu -

My gut reaction (without knowing much about what you are doing), is to keep all of the interactions in the model together.  If you believe there are multiple interactions, not including any of them could lead to improper specification of your model. Also, if there is any overlap among the interactions, you'll miss that if you test them one at a time. I'm not sure if you can do this with -inteff- though, but I know you can do it with -margins-.

Sarah

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Teemu.Kautonen@tse.fi
Sent: Wednesday, October 27, 2010 2:42 AM
To: statalist@hsphsun2.harvard.edu
Subject: RE: st: Interaction in logit

Sarah and Maarten,

Thanks very much, these were great tips. Maarten is of course right in pointing out that I should have provided full references, apologies for any inconvenience. Here are the references in case someone follows this thread and needs them:

Jaccard, James (2001) Interaction effects in logistic regression, Sage.

Norton, Edward, Wang, Hua and Ai, Chunrong (2004) Computing interaction effects and standard errors in logit and probit models. The Stata Journal 4 (2), 154-167.

I am wondering whether I could ask a follow-up question related to inteff (Norton et al. 2004) though?

Our model is, put simply, as follows:

y = a + x1 + x2 + x3 + z + x1z + x2z + x3z + c

where y is a binary response variable, a is the intercept, x1-x3 are continuous predictors, z is a binary variable that stands for two groups and c is a set of covariates.

Would it be appropriate to keep all interaction terms in the model at the same time, or would you recommend testing the interactions separately, i.e. keeping only one interaction term in the model when running inteff? Or would a completely different strategy be better for testing multiple group differences - something like a random coefficient model?

Many thanks again for your kind assistance, it is much appreciated.

Cheers

Teemu

________________________________________
From: owner-statalist@hsphsun2.harvard.edu [owner-statalist@hsphsun2.harvard.edu] on behalf of Mustillo, Sarah A [smustill@purdue.edu]
Sent: 25 October 2010 15:51
To: statalist@hsphsun2.harvard.edu
Subject: RE: st: Interaction in logit

In addition to Maartin's Stata Tip #87, UCLA also has some nice tutorials on using -margins- to interpret interactions in logistic regression.

For continuous by continuous:

http://www.ats.ucla.edu/stat/stata/faq/logitconcon.htm

For categorical by continuous:

http://www.ats.ucla.edu/stat/stata/faq/logitcatcon11.htm

For multiple interactions:

http://www.ats.ucla.edu/stat/stata/faq/margins_mlogcatcon.htm

Sarah

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Maarten buis
Sent: Monday, October 25, 2010 8:44 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Interaction in logit

--- On Mon, 25/10/10, Teemu.Kautonen@tse.fi wrote:
> My colleagues and I are working on an analysis where we
> have a dummy moderator and three continuous IVs which the
> dummy is hypothesised to moderate. The dependent variable is
> a dummy and we estimated a logit model.
>
> We have run the analysis both using the -inteff- command by
> Ed Norton and his colleagues and by analysing the odds
> ratios, as advised by Jaccard (2001).
<snip>
> Does anyone have more experience with this type of analysis
> and with these two approaches to analysing interactions in
> binary regression?

Please give complete references. This is a multi-disciplinary
list, and literature you assume so universally well known that
a "name-year" reference will suffice is likely to be completely
unknown in other disciplines.

Interactions in terms of odds ratios and marginal effects are
subtly different, in that odds ratios are effects in relative
terms with respect to the baseline odds while marginal effects
are absolute effects. This means that the interaction effects
as computed by -inteff- are sensitive to differences in the
baseline odds, while the interaciton effects in terms of the
ratio of odds ratios is not sensitive to this difference.
Sensitivity with respect to differences in the baseline odds
is not necesarily a bad thing, it is a substantive quesiton
whether or not you want to control for that. I wrote an
example of that in:

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

Hope this helps,
Maarten

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

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

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