Split by gender, or pool them into the same model? Could someone please explain to me in layman's terms the difference between the following 3 scenarios in OLS multiple regression? Let's assume my DV is income, and my IVs are White race, Asian race, age, and residence region.
1) Split the entire sample by male/female, and run the models seperately. 
2) Just run a single model, but add a control for gender (0/1).
3) Create distinct binary variables for each gender of each race, as if it's a categorical variable (e.g. White male (ref), White female, Asian male, Asian female).
So which method of these 3 is the best? And what are the reasons the other ones are not ideal? Any help would be greatly appreciated!
Thanks
 A: Each of these methods is different, and I will first explain the differences before making a recommendation.  Method (2) uses a single linear model with a main-effect term for gender, but no interaction terms.  In this model you would get a single "shift" effect for the gender variable, but since there are no interaction terms, the effects of the other IVs would be assumed to be equal for males and females.  Method (3) generalises this, and is equivalent to a model with a main-effect variable for gender, plus interaction terms.  (There is no need to construct this by creating the interaction variables individually.  In standard statistical software you can add interaction terms from the original IVs without having to manually construct these as variables.)  Method (1) is a variation of this where instead of adding interaction effects, you split the two gender groups into completely separate models.  This latter method also effectively includes variable interaction, but each model ignores the data from the other gender.
The type of model you use will depend on your objective and the nature of your available data.  For simplicity, I'm going to assume that you simply want to make a predictive model for income.  If you have sufficient data to ensure reasonable residual degrees-of-freedom, I recommend starting with a single model with a main-effects term and interaction terms for the gender variable.  That model form will give you reasonable flexibility, but you will obviously still need to check its diagnostic plots to see if the data fit the assumed model form.  As I have argued in another answer, it is generally a bad idea to split your data into multiple models; it is far preferable to have a single model that can adequately describe your entire data set.  Because you are dealing with an income variable, you might also find that you get a better model if you put it on a logarithmic scale in the linear model, or use some other model that is appropriate for this type of variable.
