Date: Tue, 16 Dec 2008 10:13:23 -0500
Reply-To: sudip chatterjee <sudip.memphis@GMAIL.COM>
Sender: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From: sudip chatterjee <sudip.memphis@GMAIL.COM>
Subject: Re: Regression: do you always need main effects with interactions?
In-Reply-To: <200812161447.mBGBl2us016546@malibu.cc.uga.edu>
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This is interesting, but the fact is, your theory will suffice you
when you are in this situation. I regularly face this situation where
I get main effects are insignificant whereas interaction effects are
significant, I never tried a model with only interaction effect
(though). I am aware of the reason behind my situation, so hopefully
lot depends on the subject on which your model is based on!
Dale provided a wonderful example. In my knowledge if interacttion
(only) makes sense then Cheers! else we can abide by the tradition.
Regards
On Tue, Dec 16, 2008 at 9:47 AM, Talbot Michael Katz <topkatz@msn.com> wrote:
> Hi.
>
> I think you missed my point, which doesn't make it valid, but let me try
> to illustrate with your example (almost).
>
> Suppose you have Y = 0.02*X1 + 0.04*X2 - 1.5*X1*X2
>
> where the crucial fact is that the coefficients of X1 and X2 are not
> significant, so that their appearance of existence is due to random
> errors. Then, when X1 and X2 are both equal to each other and between 0
> and 0.02 (0 <= X1 = X2 <= 0.02), the model with main effects says that Y
> will be positive and increasing (after 0.02 that turns around). I'm
> guessing that if the coefficients of X1 and X2 are not significant, then
> in reality, you're likely to find that Y is negative and decreasing. Then
> haven't you been misled? By the way, this leads to a fourth option on my
> original list of three, which is kind of a variation on my first one. It
> may be that even though the coefficients of X1 and X2 are not significant,
> by random error the value of Y will be positive more often than it is
> negative when 0 <= X1 = X2 <= 0.02; if you can prove that, then I'd still
> consider myself wrong.
>
> Thanks!
>
> -- TMK --
> "The Macro Klutz"
>
>
> On Tue, 16 Dec 2008 06:46:28 -0500, Peter Flom
> <peterflomconsulting@MINDSPRING.COM> wrote:
>
>>Talbot Michael Katz <topkatz@MSN.COM> wrote
>>
>>>Although I've seen several discussions on this subject, I've been
> enjoying
>>>all the different angles on this one. But so far everyone's lined up on
>>>the same side of the debate, so let me pose a straw man for the other
>>>side. I can imagine the following situation arising:
>>>
>>>positive coefficients on the main effects that are statistically
>>>insignificant, and negative coefficient on the interaction that is
>>>significant.
>>>
>>>Then there could be values of the two main effects for which it looks
> like
>>>the response should increase, but it really will decrease. If that could
>>>happen, then I'd want to eliminate the main effects terms and keep only
>>>the interaction, wouldn't I?
>>>
>>>Now, notice I said "IF" that could happen. I've been too lazy to do the
>>>math, so it just might be impossible. In that case, that would actually
>>>support the argument that main effects should be included anyway, since
>>>they couldn't conflict with observed reality.
>>>
>>>So, my challenge to you is:
>>>1) prove me wrong, i.e., show that this situation cannot arise, OR
>>>2) argue that the main effects should still be included because it is
>>>better to be misled than to defy orthodoxy (although I suppose if you
>>>believed that, you wouldn't state it quite this way), OR
>>>3) concede that there are situations in which only the interactions
>>>should be included.
>>>
>>
>>I'm sure that this circumstance in 1) could arise, but I am not sure what
> that has to do with 2).
>>
>>I think Dale came up with a very interesting case for 3) (although
> different from the one that TMK proposes), and I vaguely remember an
> article by David Rindskopf with some other examples.
>>
>>The main thing, then is point 2. How does including the main effects
> mislead you?
>>
>>You get something like:
>>
>>Y = 10 + .02 X1 + .04 X2 - 1.5 X1X2
>>
>>this tells you everything you need to know. If X1 is high, but X2 is
> low, Y is low. If X1 is low, but X2 is high, again, Y is low. Only if
> both X1 and X2 are high is Y high.
>>
>>On the other hand, if you look at the model with only the interaction you
> get something like
>>
>>Y = 10 - 1.2X1X2
>>
>>this could be saying any of a number of things: This same thing would
> arise if X1 and Y were *positively* related, or if X2 and Y were
> positively related, or if both relationships were positive and there was
> NO interaction. Thus, with this model, you don't know what is going on.
>>
>>
>>Peter
>>
>>Peter L. Flom, PhD
>>Statistical Consultant
>>www DOT peterflom DOT com
>
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