why multinom() predicts a lot of rows of probabilities for each level of outcome?

Question

I have a moltinomial logistic regression and the outcome variable has 6 levels: 10,20,60,70,80,90

test<-multinom(y ~ x1 + x2 +  as.factor(x3) ,data=data1)

I want to predict the probabilities associate with each level of y for each set of given input values. So I run this:

 dfin <- data.frame( ses = c(10,20,60,70,80,90), x1=2.1, x2=4, x3=40)
 predict(test, todaydata = dfin, type = "probs")

But instead of getting 6 probabilities (one for each level of outcome), I got many many rows of probabilities. Each row has 6 probabilities (summation is 1) but I don't know why I get many rows and which row I should trust.

5541   7.226948e-01 1.498199e-01 8.086624e-02 1.253289e-02 8.799416e-03 2.528670e-02
5546   6.034188e-01 7.386553e-02 1.908132e-01 1.229962e-01 4.716406e-04 8.434623e-03
5548   7.266859e-01 1.278779e-01 1.001634e-01 2.032530e-02 7.156766e-03 1.779076e-02
5562   7.120179e-01 1.471181e-01 9.146071e-02 1.265592e-02 8.189511e-03 2.855781e-02
5666   6.645056e-01 3.034978e-02 1.687687e-01 1.219601e-01 3.972833e-03 1.044308e-02
5668   4.875966e-01 3.126855e-02 2.090006e-01 2.430828e-01 3.721631e-03 2.532970e-02
5670   3.900772e-01 1.305786e-02 1.803779e-01 4.137106e-01 1.314298e-03 1.462155e-03
5671   4.272971e-01 1.194599e-02 1.748494e-01 3.833422e-01 8.863019e-04 1.678975e-03
5674   5.477521e-01 2.587478e-02 1.650817e-01 2.487404e-01 3.368726e-03 9.182195e-03
5677   4.300207e-01 9.532836e-03 1.608679e-01 3.946310e-01 2.626104e-03 2.321351e-03
5678   4.542981e-01 1.220728e-02 1.410984e-01 3.885146e-01 2.670689e-03 1.210891e-03
5705   5.642322e-01 1.830575e-01 5.134181e-02 8.952808e-04 8.796467e-03 1.916767e-01
5706   6.161694e-01 1.094046e-01 1.979044e-01 1.095385e-02 7.254592e-03 5.831323e-02
....

Am I missing anything in coding or do I need to set any parameter?

Answer 1

It is returning the probability for the observation to be in each of the classes. That is how multinomial logistic regressions are implemented. You can imagine a series of binomial logistic regressions (one for each class) and then choosing the class that has the highest probability. This is called the one-v-all approach.

In your example, observation 5541 is predicted to be class 1 because the first column has the highest value (probability). Observation 5670 is class 4 because that's the column with the highest probability. The matrix will have dimensions # of observations x # of classes.