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More precisely. The dataset that I'm using contains individual level data on the characteristics of voters (categorical variables) and the party they voted for (nominal variable). I'd like to find out how well does a characteristic explain variation among parties voted for. In the long run I'd like to acquire a numerical expression that describes this for certain groups of individuals, or countries in my case.

What I tried using Stata. I used linear regression where dependent variable was the characteristic and independent variable the party as a set of dummy variables (factor variable in Stata, e.g. "i.party" ). This gave me theoretically expectable results and an numerical expression (r2) for every country. However, notice that party in this case is independent variable, which is theoretically absurd, but Stata does not allow using factor variable as a dependent variable. I also tried multinomial logistic regression, but it does not seem to produce an elegant way to compare countries in the explanatory power of a characteristic.

What I'd like to know is if there's a specific method that could be applied to solve my problem? Also, since r2 indicates the same relation between two variables regardless of which variable is defined as independent and which as dependent, would it be wrong to interpret r2 in both ways?