Timeline for Can the interaction term of two insignificant coefficients be significant?
Current License: CC BY-SA 3.0
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| Nov 1, 2013 at 17:01 | comment | added | Vincent | @jbowman Hi, I also got such problem in a project last year, but I thought in such case Y=A*B, it seems that using log transformation for both sides lm(log(Y)~log(A)+log(B)) is more suitable, with less terms, variance. And the diagnostic plots are more "nice" (valid), while the residual plots of Y~A+B+A:B is still concave like. But in my project, some maths logic can be shown to use log for both sides. What if other project without too much prior knowledge? Forward selection seems may not be able to include A:B sometimes in such case, while backward must be able. | |
| Feb 12, 2012 at 16:23 | history | edited | Macro | CC BY-SA 3.0 |
changed to a conditional expectation, as is traditionally written in regression models
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| Feb 12, 2012 at 15:05 | comment | added | jbowman | I'm not so sure about that; in many cases, once you include an interaction term, A and B become unimportant. A simple example is estimating the weight of a tree based on its height and diameter at its base; once you multiply the two terms, the individual terms will drop out (although w/o the interaction, they would both be significant.) Often you need more than one gene for a trait to express itself (e.g., two blue-eyed parents for a blue-eyed child), or you need a gene and an environmental factor together for an effect to occur. Not so sure about the social sciences, though... | |
| Feb 12, 2012 at 14:46 | vote | accept | Tom | ||
| Feb 12, 2012 at 14:46 | comment | added | Tom | Thanks, this is an excellent answer! If I would have rephrased "significant" to "has explanatory power", would the answer be different? My intuition tells me that if A cannot explain Y, and B cannot explain Y, then A * B cannot explain Y either (or this is extremely unlikely). Basically I have a whole set of variables, of which many are insignificant. I would like to generate a set of interaction variables that are likely to have an impact, and was hoping that I could leave out all insignificant explanatory variable sets. | |
| Feb 12, 2012 at 14:19 | history | answered | jbowman | CC BY-SA 3.0 |