Is a win-lose model for three Presidential primary candidates appropriate? Multinomial Logit model?

Question

I have a dataset where each record represents a collection of variables for each of the counties in New York. Five variables represent the number of tweets in that geographic area for each candidate in the presidential primary races.

Bernie_tweets, Clinton_tweets, Cruz_tweets, Trump_tweets, Kasich_tweets

I am trying to evaluate the significance of tweets for each candidate and their performance in the primary(within their related Party).

Other variables that I have are; Males over 18, Females over 18, Total Population, TotalPopulation Over 18, Area(sqMiles), Median Income, etc.

I am trying to determine how to model a winner for three candidates. I believe what I should be doing is modeling it as a multinomial logit model, or something of that nature(or as a binomial model for winners of a two-horse race).

I was able to use R to make a linear regression model, for which some of the tweets were significant when modeling the actual number of votes. But I was modeling each candidate's performance individually. But I am unclear at whether or not I am approaching this problem in a correct way.

Answer 1

The two-horse-race should be modeled as a binomial logistic model, with Candidate 1 winning coded as a 1, and Candidate 2 coded as 0, Using (in R):

glm(..., family = 'binomial')

The answer to this question is the 3-horse-race of (Trump, Kasich, Cruz) should be modeled as a Multinomial logit model, coding a win for Candidate 1 as 1, Candidate 2, as 2, and Candidate 3 as 3.

Then using R (as mentioned in the last paragraph), this website provides a walkthrough of how to model the outcomes of the race. http://stats.idre.ucla.edu/r/dae/multinomial-logistic-regression/

ml$prog2 <- relevel(ml$prog, ref = "academic")  
# ref sets "academic as the first argument, not sure why that matters
# for my code, "academic" might be Candidate 1 , unsure of logic behind which candidate.
test <- multinom(prog2 ~ ses + write, data = ml)