Comparing independent variables in different models with the samen depedent variable

[Harry Gommans]

Hello,

I am running three multiple linear regression models. In all three, the dependent variable is the democracy index score of a range of countries over several years that the EU has agreements with. I use three independent variables in each model. Two of those are the same in each model: a sum of imports and exports from and to the EU divided by the GDP of the country, and a score on network governance with the EU. However, the third independent variable is a binary variable which tells whether the country has a particular agreement with the EU in force or not. In each model, this is a different agreement type (there are 3 of those agreements possible (an SAA, an AA, and a CPA), hence 3 models). A country can only have one of the particular agreements in force at a time, or it can have no agreement at all in force. The three models thus look like this:
M1:

• M1:
  • IV: democracy score
    • DV1: SAA
    • DV2: (imports+exports)/gdp score
    • DV3: network governance score
• M2:
  • IV: democracy score
    • DV1: AA
    • DV2: (imports+exports)/gdp score
    • DV3: network governance score
• M3:
  • IV: democracy score
    • DV1: CPA
    • DV2: (imports+exports)/gdp score
    • DV3: network governance score

My question is: how can I compare the independent variables of the different models among each other? For example: if both SAA and AA are positive and significant, but the SAA in model 1 has a higher beta-value than the AA in model 2, is it possible to say that the SAA accounts for a higher variance in the democracy scores overall?

If anything is unclear or you need more information, please let me know.

Best, Harry

[Joseph Coveney]

Could you do something along the following lines?

label define Agreements 1 SAA 2 AA 3 CPA 0 None
encode agreement, generate(agr) label(Agreements)
replace agr = 0 if missing(agreement)
regress democracy_score i.agr##c.DV2 c.DV3 i.agr#c.DV3

You could inspect the slope terms directly in the regression output table, or use test, margins etc. afterwards.

[Harry Gommans]

Sorry, I mixed up the IV and DV by the way, so obviously the democracy score is the DV and the other variables are IVs. The question remains the same.