Inferences about non-overlapping lines

Question

So... let's say I have data that look something like this...

(as I look at it now, in the actual data the red line is about 20% shorter than the black (at the high end... but you get the idea)

I've made a mixed effects model (lmer) where there's an effect of the x-predictor and and also an effect of the two colours. I'm thinking that if I have centred the x-axis in my model that comparisons between the colours is perfectly fine. Should I be concerned that someone may argue that only the overlapping parts on the x-axis be allowed in the comparison across colours? The lines aren't perfectly parallel but the interaction is as near 0 as one can get.

Answer 1

I think that if you did show a difference between the two groups one might generate an argument against the analysis that the true function might be non-linear and you're simply fitting different pieces of it. However, since you don't find a difference, I can't think of any scenario where the conclusion of no difference is compromised by lack of complete overlap on x.