I have a theoretical question regarding model building. I have some real empirical data, but I will present the problem in more general terms.
I have two groups. I have a dependent variable, and an independent variable.
For one group the relationship between continuous independent variable and the dependent variable looks this way:
For the second group it looks this way:
Does it make sense to include both groups in one regression model (coded as dummy variables)?
a) Will the effects for each group not cancel each other out making it harder for the model to converge? (my model actually does not converge, which is why I am asking this question - could this be the reason?)
b) as far as I understand, dummy variables change the intercept, and the slope remains the same. If I know that the slopes are so drastically different for the two groups, does it make sense to put them in the same regression model? (I assume the slope would not be correct for either group)
c) I am aware that I can introduce interaction terms, to look at the effects for groups separately. but... would just building two separate models, one for each group be wrong?