```Date: Tue, 16 Dec 2008 10:13:23 -0500 Reply-To: sudip chatterjee Sender: "SAS(r) Discussion" From: sudip chatterjee Subject: Re: Regression: do you always need main effects with interactions? Comments: To: Talbot Michael Katz In-Reply-To: <200812161447.mBGBl2us016546@malibu.cc.uga.edu> Content-Type: text/plain; charset=ISO-8859-1 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 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 > wrote: > >>Talbot Michael Katz 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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