# Multinomial logistic on grouped data with nnet package, R

This link from UCLA.edu (https://stats.idre.ucla.edu/r/dae/multinomial-logistic-regression/) provides a useful example for a multinomial logistic case. However, I wonder how can I correctly interpret the coefficients in case of grouped data. Here is an example following the ucla.edu exercise:

# Load packages
require(foreign)
require(nnet)
require(ggplot2)
require(reshape2)
str(ml)
# $prog : Factor w/ 3 levels "general","academic","vocation": 3 1 3 3 3 1 3 3 3 3 ... #$ write  : num  35 33 39 37 31 36 36 31 41 37 ...
# $ses : Factor w/ 3 levels "low","middle","high": 1 2 3 1 2 3 2 2 2 2 ...  NOTE: I wish to predict variable prog using the numeric variable write and the 3 level factor ses. I don't care if the 3 levels, "low", "middle", "high", are ordered! As far as I am concerned this factor can be gender or country or whatever. # Choose the baseline level of 'prog' dependent variable ml$prog2 <- relevel(ml\$prog, ref = "academic")


I run a simple model based only on 'write' independent variable (I.V.)

test1 <- multinom(prog2 ~ write, data = ml)
summary(test1)
# I get the following coefficients
Coefficients:
(Intercept)       write
general     2.712485 -0.06600782
vocation    5.359000 -0.11780909


I run the complex model, including 'ses' factor as the second I.V.

test2 <- multinom(prog2 ~ write + ses, data = ml)
summary(test2)
# I get the following coefficients
Coefficients:
(Intercept)      write  sesmiddle    seshigh
general     2.852198 -0.0579287 -0.5332810 -1.1628226
vocation    5.218260 -0.1136037  0.2913859 -0.9826649


So, how can I directly get the intercepts for each level of ses? I am not interested in the change of intercept from one level to another.

I tried this:

test3 <- multinom(prog2 ~ write + ses -1, data = ml)
summary(test3)


which is interpreted by R as omitting the 'main' intercept

Coefficients:
write   seslow sesmiddle  seshigh
general  -0.05792787 2.852149  2.318866 1.689318
vocation -0.11360180 5.218146  5.509562 4.235464


As I see, the intercept of model test2 is actually the coefficient of level low of factor ses in model test3 (the first level in alphabetical order).

So, now, can I make the interpretations like this:?

The log odds of being in general program vs. in academic program will increase by 2.85 for ses=low, by 2.32 for ses=middle and by 1.69 for ses=high. In a similar way for the log odds of being in vocation program vs. in academic program: the increase will be by 5.22 for ses=low, by 5.51 for ses=middle and by 4.24 for ses=high.

Sorry if my question might look naive.