[R-sig-DCM] Inclusion of interaction without its main effect

[Chris Chapman]

Of course it depends on the model ... but in general I'd say, "yes, if it 
makes sense for your problem."  As Marcel showed below, an interaction term 
could be considered to be simply a different variable.  It happens to be 
highly collinear with some other variables, but that does not change its 
status as a variable that is perfectly reasonable if used sensibly (which 
means -- if it's constructed -- taking account of scaling issues, 
heterogeneity of measurement error, etc.)

OTOH, *interpreting* an interaction term can be a problem.  There are cases 
like Marcel's where it may be clearer than the (so-called) main effects, but 
for my 0.02, interaction terms in DCM models  are often quite difficult to 
conceptualize, explain, or act upon. So in practice I tend to avoid them 
unless there is a good reason to think they're needed ("price:brand" is 
perhaps a common one to consider).

-- chris

--------------------------------------------------
From: "Dimitri Liakhovitski" <dimitri.dcm at gmail.com>
Sent: Wednesday, February 23, 2011 3:24 PM
To: "Marcel Gerds" <marcel.gerds at berkeley.edu>
Cc: <r-sig-dcm at r-project.org>
Subject: Re: [R-sig-DCM] Inclusion of interaction without its main effect

> I have a general follow-up question to everyone.
> Is this "legal" to include interaction terms while excluding the main
> effects?
>
> Dimitri
>
> On Wed, Feb 2, 2011 at 4:17 PM, Marcel Gerds 
> <marcel.gerds at berkeley.edu>wrote:
>
>> I withdraw the question. I have just figured it out myself.
>> One has only to create a variable which includes the interaction:
>>
>> interact <- cost_a / income
>>
>> This new variable can then be included in the model without having the
>> respective main effect in the model.
>>
>> mlogit.model <- mlogit ( choice ~ interact + cost_b , data = data _ ml )
>>
>> Best regards,
>> Marcel
>>
>>
>>  Dear fellow DC modellers,
>>>
>>> I want to include an interaction term as an explanatory variable without
>>> having its main effect in the model. For example, I run
>>>
>>> mlogit.model <- mlogit ( choice ~ cost_a / income + cost_b , data = data 
>>> _
>>> ml )
>>>
>>> where two kind of cost are used as explanatory variables for choosing an
>>> alternative. Income is a subject-specific variable. However, if I run 
>>> this,
>>> R not only includes cost_b and cost_a:income in the model, but also 
>>> cost_a.
>>> Is there a way to suppress the inclusion of a main effect when one wants
>>> to add only its interaction?
>>> Thanks for any help.
>>>
>>> Best regards,
>>> Marcel
>>>
>>
>> --
>> Marcel Gerds, M.Sc.
>> University of California
>> Department of Agricultural and Resource Economics
>> 233 Giannini Hall
>> Berkeley, CA 94720
>>
>> Tel.:  +1 510-643-2202
>> Mobil: +49 176 21302825
>>
>> E-Mail: marcel.gerds at berkeley.edu
>> web:    www.marcel-gerds.de
>>
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