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Re: st: interaction effect without one of main effects


From   "Clive Nicholas" <Clive.Nicholas@newcastle.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: interaction effect without one of main effects
Date   Thu, 17 Feb 2005 22:07:14 -0000 (GMT)

Mary Lee wrote:

> Stata has a unique option in -xi-
> i.varname1|varname3 creates dummies for categorical
> variable varname1 and includes continuous varname3:
> all interactions and main effect of varname3, but not
> main effect of varname1. I'm wondering when we can use
> this option. Don't we have to always include both main
> effects in the model if we want to estimate the
> associated interaction effect??

Formally, _all_ lower-order terms have to be included in such
'hierarchical' regression models (somebody else can slap me down if this
phrase is inappropriate in this context). So, if your model contains
X1*X2, both X1 _and_ X2 must be included as well. This is necessary,
because omitting any of the main (singleton) effects could have a large
(and misleading) impact on the remaining coefficients. Some may say that
one unfortunate side-effect of including all of these is the greatly
inflated multicollinearity that it introduces into the model.

> Stata manual gives the following example,
> xi: logistic outcome bp i.agegrp|weight
> My guess is that we can use such a specification if
> our focus is to examine the effect of 'weight' on
> 'outcome' which is conditional on 'age grp', while the
> main effect of 'agegrp' on 'outcome is not
> theoretically meaningful. Yet, I'm not statistically
> or theoretically convinced whether we are allowed to
> estimate the interaction effect without one of the
> main effects. I tried to find out any statistical and
> theoretical justifications for such a model
> specification, but no success....

See above and below for this one.

> Can anyone help me understand the usage of
> 'i.varname1|varname3'? How do I interpret the result
> of the interaction term in this case? Are there any
> books or articles explaining the interaction effect
> without the main effect?

Essentially, you are investigating whether the effect of X1 on Y varies by
units of X2. For instance, if my response variable is the propensity to
vote at the _next_ election (out of 100) and my key predictor is whether
or not they turned out at the _last_ election (0 = no; 1 = yes), an
interesting covariate which may intervene upon this relationship is age.
If we propose an interaction effect, we are allowing for the possibility
that, in this example, past turnout behaviour may be stronger for older
(younger) voters than they are for younger (older) ones.

A good (pre-publication) paper to look at which covers the basic merits,
'dos' and 'donts' of interaction effects, together with a checklist, has
been prepared by Bear Braumoeller (another member of Statalist) which you
can view at:

http://www.people.fas.harvard.edu/~bfbraum/

It can be found under the 'statistical methodologies' section. Also, two
nice little monographs that are devoted entirely to this topic are by
Jaccard, Turrisi and Wan (1990) and by Jaccard (2001).

I hope all this helps.

CLIVE NICHOLAS        |t: 0(044)7903 397793
Politics              |e: clive.nicholas@ncl.ac.uk
Newcastle University  |http://www.ncl.ac.uk/geps

References:

Jaccard J, Turrisi R and Wan C (1990) INTERACTION EFFECTS IN MULTIPLE
REGRESSION, QASS Series Paper 07-072, Thousand Oaks, CA: Sage.

Jaccard J (2001) INTERACTION EFFECTS IN LOGISTIC REGRESSION, QASS Series
Paper 07-135, Thousand Oaks, CA: Sage.

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