I estimate some logistic and OLS models on big survey data (overfitting shouldn't be a problem) where I need to control for a country of a respondent. The country variable is coded as iso3n- 3 digits for every unique country (there are 96 individual countries in my data). Important thing is that I only want to control for a country effect, I'm not interested in the significance or parameters of every individual country.
I wonder what is the theoretical reason to code country as 96 dummies with additional base level. Why couldn't I just treat the nominal country variables as quasi-linear and thus control for its effect on my other variables?
I already tried to estimate two models in R; one with dummies and one with a single nominal "country" variable but estimated parameters of my key independent variable differ. Why is that? I also searched the site but most entries on the subject just assume that dummy coding is needed.