Why is an interaction term better than two regressions?

[ObviousScully]

I have struggled with the "because it is" and vague answers on this topic for a while and I was hoping someone could actually give a real reason why using an interaction term in regression is better than doing two regressions.

For example:

While doing a GLM to see how environmental factors predict a species probability of use between seasons, what benefit is gained by using one data set while including a seasonal interaction factor instead of two regressions using data from one season in each.

Any guidance on this would be appreciated.

 

[katxt]

It could tell you if the regression lines are significantly different or not. Would that be helpful?

 

[ObviousScully]

Thank you for your response katxt.

I suppose I am talking more generally. I have been told not to do one and to do the other but I have never had it explained why.

Why would it be worse to use two sets of data that are different temporally for their own regression be worse than using the data combined but using an interaction covariate for that temporal difference?

Does that question make sense?

 

[katxt]

Purists would say that there are more error df in the glm. This could mean loss of power doing separate regressions if the effects are small. I suppose that it is like doing a 2 way anova vs doing two individual t tests.
No doubt there are situations where the two regressions would be better if the glm assumptions are not met.
Generally I prefer the method which is easiest to explain and interpret so long as the results are satisfactory. Also, some people are just fussbudgets.

 

[Karabiner]

I have struggled with the "because it is" and vague answers on this topic for a while and I was hoping someone could actually give a real reason why using an interaction term in regression is better than doing two regressions.

It depends on the research questions which you want to answer.

If for example you want to know whether a specific predictor is
more closely related with outcome in one group than in another
group, then you have to test this directly.

And there certainly are research questions which can be answered by
two separate regressions.

With kind regards

Karabiner

 

[ObviousScully]

Thank you so much for both of your responses!

It depends on the research questions which you want to answer.

If for example you want to know whether a specific predictor is
more closely related with outcome in one group than in another
group, then you have to test this directly.

And there certainly are research questions which can be answered by
two separate regressions.

With kind regards

Karabiner

If I am reading your response correctly, you are saying there may be sometimes when two regressions would work but in those cases as well as ones where you want to know if a specific predictor is more closely related with an outcome in one group than another using an interaction factor would be appropriate.

Is this correct? Or are there scenarios where an interaction factor would be less appropriate than two regressions?

-Arthur

 

[Karabiner]

I do not know any. I only know scenarios where no question regarding
different regression slopes (different regression weights) is asked. But
if you want to know whether a regression coefficient varies between groups
statistically significantly, then you need to test this. An important ascpect is
discussed here.

With kind regards

Karabiner

 

[ObviousScully]

Thank you so much for all this information.