Main effects vs. interaction - what comes first?

#1
Hello everyone,

I have a burning question about reporting model results:
Should the main effects or their interaction be reported first?

If you have any sources to support your opinion, please feel free to share!
 

noetsi

Fortran must die
#2
The answer is to look at the journal you intend to submit to or the style manual they use (like APA). :)

I don't think there is a correct answer to this. Main effects, while you should retain them in the model, don't matter at all when there is significant interaction.
 
#3
Thank you so much! :)

This is also what I was taught during my master's. But my thesis examiners (different subject, different university) quite abruptly told me that I am in the wrong, and that this indeed is not a matter of preference - they claim that interactions should be reported first, and then followed by the main effects. I think (from what I was taught) that main effects matter less, so this would justify reporting them first. Sort of like an intro into the more refined result - i.e., the interaction. This is what I have always done, and no one ever objected.

I will now have to do as they demand for obvious reasons, but I would still like to support this with some sort of proof that I am not completely unhinged.
 

Karabiner

TS Contributor
#4
hlsmith told you the same thing as your examiners.

first order effects change their meaning there is an interaction.
I think (from what I was taught) that main effects matter less, so this would justify reporting them first.
That seems to contradict what you have said before.

With kind regards

Karabiner
 
#5
hlsmith told you the same thing as your examiners.

first order effects change their meaning there is an interaction.

That seems to contradict what you have said before.

With kind regards

Karabiner

What do you mean he said the same thing?
He said there is no correct answer (which is what I told the examiners essentially), and the examiners believe that there is one correct answer, which is - report the interaction first. What I would say/have said is what makes more sense to me (and what I was taught) is to first report the main effects, and then the interaction. As the interaction sort of overrides the main effects on their own.
 

hlsmith

Less is more. Stay pure. Stay poor.
#6
Well I was accidently beckoned... So I will weigh in. I've been informed that the interaction term is the 'most-est important-est" and main effects should be in the model but lose some interpretation, since they are conditional.

I will add, that in my old age, I now better appreciate providing all terms (estimates), including the intercept. This way the reader can calculate the estimates for all groups combinations. For example if I had an interaction between gender and a gene, I would be able using all the terms to calculate the estimates for the base case (females, no gene), females with gene, males no gene, and males with gene. So all of the components to create a disordinal plot of the interaction.
 

noetsi

Fortran must die
#7
I have read that main effects have no meaning when there is interaction. Or can not be interpreted easily anyhow. But that has nothing to do with how they are reported. How they are reported is a style not statistical issue.
 
#8
If you have interactions in the model, then both interactions and main effects should be reported at the same time.

As a reference the classic book by Box, Hunter, Hunter "Statistics for Experimenters"
 
#9
Thank you all for replies! :)
Yes, I agree that both should be reported (even if the main effects are non-significant)!
And the interaction is the most-est important-est :) I agree!
I also agree that how they are reported is more to do with style than stats!
Has anyone ever been confronted about this, with the other person saying that the only correct way to report these results is to start with the interactions and then move on to the main effects?
 

noetsi

Fortran must die
#10
Thank you all for replies! :)
Yes, I agree that both should be reported (even if the main effects are non-significant)!
And the interaction is the most-est important-est :) I agree!
I also agree that how they are reported is more to do with style than stats!
Has anyone ever been confronted about this, with the other person saying that the only correct way to report these results is to start with the interactions and then move on to the main effects?
I have not, but most likely you would in a journal. My research was not in statistics.
 

hlsmith

Less is more. Stay pure. Stay poor.
#11
Basing anything solely on significance is likely to get a person in trouble. Of note, if it wasn't a planned analysis a priori, it could be spurious. It can take say 4 times as much data to power a interaction test (significance) as a main effect. So some posit they may not be generalizable if they weren't a planned/powered test.
 
#12
Has anyone ever been confronted about this, with the other person saying that the only correct way to report these results is to start with the interactions and then move on to the main effects?
No, I have not experienced that.

It would seem quite bizarre to just report the the interaction effect and not the main effect and not the intercept.

If you have a model like this:

y = intercept + A + B + A:B + residual

then of course you need to report the whole model:

intercept + A + B + A:B

A factorial model can be defended by the multi variable Taylor expansion. Look at Box Hunter Hunter and their writings. or Box Draper (Empirical model building)

It is often said in this kind of literature, that if you include a higher order interaction effect, then you should always include lower order interaction effects and main effects.

If the people around you still questions this, then suggest to consult a statistician. (But don't make your supervisors loose their face! Very important!)
 
#13
Thank you everyone for your answers!
I have changed my thesis, and put the interactions before the main effects, just to avoid tensions.
Hopefully no one will even read my thesis after it's accepted, but if they do, I hope they don't think any less of me for this small weirdness (after all, there are much more substantial things to judge me for in there!)!