Logistic Regression Models Without Main Effects?

#1
Hi there, I am building logistic regression models measuring human behaviour, which consist of categorical variables: demographics, conditions, and interactions between the demographics and the condition variable.

The big issue is that as per my theory tested I am not interested at all in the main effects of demographics but only in the interactions with the condition variable. Moreover, there are extreme collinearity forces among the demographics e.g. income and education etc.

Hence, I would intend to present log models without main effects in my thesis. Do you think this can be defended? If so, could you please give me ideas or statistical arguments of how to argue in favour of that?

Thanks in advance,
P
 

ondansetron

TS Contributor
#2
I don't think it's very reasonable to exclude main effects. By definition, if the interaction is important, you've specified that the variables are important for illustrating the relationship accurately. As a general principle, it's not good to test main effects or lower order terms after a higher order term or interaction is significant (or deemed theoretically necessary).

For future advice, it's probably good to at least seek out advice from the contrary side, but often both positions. You run the risk of confirmation bias and proceeding down the wrong path by asking someone to agree with you. Doing this in research is dangerous in that you may find yourself trying to justify results and estimates after seeing the data, so you can "confirm" something. All too often, I see researchers excluding or including analysis based on whether it agrees with what they wanted or expected to see. (Not that you're doing this, but it's somewhat related).
 

ondansetron

TS Contributor
#3
Also, there are ways to handle collinearity if you need to make inferences on the beta estimates (ridge regression, possible centering,
partialling out a variable you don't care about, dimension reduction).

It is also not advisable, for estimation purposes, to exclude variables that are unimportant to you but are reasonably expected to "impact" the DV.
 

hlsmith

Not a robit
#4
Standard practice is to include main effects even if you don't think you care about them. The relationship between the variables is conditional. Side note, Andrew Gelman posted yesterday on his forum that you need, I think, 16 times more data if you want to include an interaction term in the model. This was from an example not a general rule, but was supposed to emphasize the point that adding interaction terms requires substantial more data.

As odansetron mentioned, people like to center data when possible to alleviate collinearity affects.
 

ondansetron

TS Contributor
#5
Standard practice is to include main effects even if you don't think you care about them. The relationship between the variables is conditional. Side note, Andrew Gelman posted yesterday on his forum that you need, I think, 16 times more data if you want to include an interaction term in the model. This was from an example not a general rule, but was supposed to emphasize the point that adding interaction terms requires substantial more data.

As odansetron mentioned, people like to center data when possible to alleviate collinearity affects.
Another note is that you will have to work with your data to determine which method of relieving collinearity is best. Centering may work in some cases and note in others, depending on the variable, whereas a ridge regression may be worth while in other cases.
 

Dason

Ambassador to the humans
#6
One thing I like to ask people who want to build models like these is what do you think the interaction term represents in your model if you don't include main effects? What it actually represents is probably radically different from what you want it to represent. Is the slight increase in degrees of freedom really worth having something you really don't know how to interpret?
 

hlsmith

Not a robit
#7
I havent really figured it out but I have heard some experts in conferences saying in their life they haven't ever seen a real interaction. I don't know if they mean the interaction is just a proxy of something else.