How to Interpret a Coefficient table for Multinom() Function in R

Question

I have a dataset that has weather=0 if temp is <65 degrees Fahrenheit, weather = 1 if temp is =65 degrees Fahrenheit, and weather = 2 if temp is >68 degrees Fahrenheit. I need to estimate a probability that the temp is between 65 <= weather < 68 degrees Fahrenheit, given the days = 20. Here is the formula and output

multinom(formula = weather ~ days, data = USWeather13)

Which gives the coefficient table:

Coefficients:
      (Intercept)              days
1        5.142                -.252
2        25.120                .343

Std. Errors: 
      (Intercept)              days
1        1.742                 .007
2        1.819                 .004

Does anyone know how I can interpret this or figure out this problem?

Answer 1

In your example, weather=0 is the reference level, and you have the coefficients as the log odds ratio of weather=1 or weather=2 for every unit of your predictor Days .

It's an example without the complete information, but reading your coefficients, it means for every unit increase in days, you reduce the log-odd probability of 1 vs 0 by -.252 and log-odd probability of 2 vs 0 by.343.

If you need to figure the respective probabilities at days=20, you do:

fit = multinom(formula = weather ~ days, data = USWeather13)
predict(fit,newdata=data.frame(days=20),type="prob")

Think this website might provide a good guide on how to interpret the coefficients.