Compare independent variables among different models with same dependent variable

[tnroo]

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:
  • DV: democracy score
    • IV1: SAA
    • IV2: (imports+exports)/gdp score
    • IV3: network governance score
• M2:
  • DV: democracy score
    • IV1: AA
    • IV2: (imports+exports)/gdp score
    • IV3: network governance score
• M3:
  • DV: democracy score
    • IV1: CPA
    • IV2: (imports+exports)/gdp score
    • IV3: 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?

 

[Karabiner]

You could perform an analysis of covariance with the two covariates (imports+exports)/gdp score and network governance score, and with agreement type as a factor with 4 levels. If the factor has a statistically significant association with democracy score, then you can perform pairwise comparisons between the adjusted means or marginal means of the 4 levels.

With kind regards

Karabner