Hi All,
I would like to compare the effect of an explanatory variable (say X1) on a response variable (Say Y) between two geographic regions in which one is a sub-region of the other. For example, I am fitting two regression models(Y on X1), one for the city data and the other for country data, where city belongs to the same country. But the distributions of X1 and Y are different between these regions (though one is nested in the other).
  1. Would the comparison of regression coefficients of X1 between two models make sense to assess the strength of two effects? (if the coefficient of X1 in city is higher, can we say the effect of X1 on Y is higher in city than country)
  2. Or, since distributions vary between regions, should we use standardized coefficients for the comparison of effects?
  3. Or is there any other advanced method to address this situatio

Any help on this is highly appreciated.