# Dummy variable + interaction term or stratified analysis with survey data

I have data where each observation is an individual. Each individual has a value for country, a factor variable. There is a sampling weight variable to make the sample from each country representative of that country's population.

I want to compare Y ~ X between countries. Given that the weights are calculated for each observation to reflect country-level population distributions, would my results be valid if I:

Conduct a multiple linear regression with country as a dummy variable and an X*Country interaction term:

$$Y = \beta_{0} + \beta_{1}X + \beta_{2}Country + \beta_{3}X*Country + \epsilon$$

or should I stratify my analyses by countries 1-n and compare regression coefficients

$$Y_{country1} = \beta_{country1_0} + \beta_{country1_1}X_{country1} + \epsilon_{country1}$$

...

$$Y_{countryn} = \beta_{countryn_0} + \beta_{countryn_1}X_{countryn} + \epsilon_{countryn}$$

Or should I be looking into a different method entirely?

I realize that $$\beta_{countryi_1} = \beta_{1} + \beta_{3}$$ but I'm not sure about my standard errors/validity.

Thanks!

• this link could help – Dan Chaltiel Mar 6 '19 at 7:54
• Thanks! this is a good reference in general, but I unfortunately do not know how the weights were constructed so a model based approach is off the table. – NY stats guy Mar 6 '19 at 18:33
• This is more of a question about use of interaction terms or separate regression models. This topic has been discussed extensively here on CV. The answer is, it depends on what you are trying to do. stats.stackexchange.com/… – StatsStudent Mar 10 '19 at 14:36
• So it seems, I just wasn't sure if the weighting scheme for the data would influence this. But many of the other threads are helpful- thanks – NY stats guy Mar 12 '19 at 22:06