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Multinomial Logistic Regression in R

Last Updated : 09 Jun, 2023
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In this article, we will learn about Multinomial Logistic Regression which can be used when we have more than two categories in the target column. Let’s first start with a little bit brief explanation about the multinomial logistic regression and after this we will move on to the code implementation part by using different packages which are available in R.

What is Multinomial Logistic Regression?

Multinomial logistic regression is used when we have a categorical dependent variable with more than two categories. In R, we can perform multinomial logistic regression using the multinom() function from the nnet package.

  • Multinomial logistic regression is a type of regression analysis used to predict the nominal or categorical dependent variable with two or more levels. 
  • the multinom() function from the nnet package can be used to perform multinomial logistic regression.

VGAM Package in R for Multinomial Logistic Regression

The VGAM (Vector Generalized Linear and Additive Models) package in R Programming Language provides a suite of functions for fitting a variety of regression models. The vglm() function is one of the most commonly used functions in the package and can be used for multinomial logistic regression.


# Load the iris dataset
# Convert the species variable to a factor
iris$Species <- as.factor(iris$Species)
# Fit a multinomial logistic regression model
fit <- vglm(Species ~ Sepal.Length 
            + Sepal.Width
            + Petal.Length
            + Petal.Width,
            data = iris,
            family = multinomial)
# Print the model summary


             Estimate Std. Error z value Pr(>|z|)  
(Intercept):1     35.490  22666.953      NA       NA  
(Intercept):2     42.638     25.708   1.659   0.0972 .
Sepal.Length:1     9.495   6729.217      NA       NA  
Sepal.Length:2     2.465      2.394   1.030   0.3032  
Sepal.Width:1     12.300   3143.611      NA       NA  
Sepal.Width:2      6.681      4.480   1.491   0.1359  
Petal.Length:1   -22.975   4799.227  -0.005   0.9962  
Petal.Length:2    -9.429      4.737      NA       NA  
Petal.Width:1    -33.843   7583.502      NA       NA  
Petal.Width:2    -18.286      9.743      NA       NA

nnet Packgae in R for Multinomial Logistic Regression

We can also define a neural network using nnet package in R and in the neural net we can have more than two output categories by including that many numbers of nodes in the output layer of the neural network.


# Fit multinomial logistic regression model
model <- multinom(Species ~ Petal.Length
                  + Petal.Width
                  + Sepal.Length
                  + Sepal.Width,
                  data = iris)
# Predict flower species for new data
new_data <- data.frame(Petal.Length = 1.5,
                       Petal.Width = 0.3, 
                       Sepal.Length = 4.5, 
                       Sepal.Width = 3.1)
predict(model, newdata = new_data, type = "class")


# weights:  18 (10 variable)
initial  value 164.791843 
iter  10 value 16.177348
iter  20 value 7.111438
iter  30 value 6.182999
iter  40 value 5.984028
iter  50 value 5.961278
iter  60 value 5.954900
iter  70 value 5.951851
iter  80 value 5.950343
iter  90 value 5.949904
iter 100 value 5.949867
final  value 5.949867 
stopped after 100 iterations

The iris dataset contains measurements of petal and sepal length and width for three different species of flowers (setosa, versicolor, and virginica). We fit the multinomial logistic regression model to predict flower species based on the four measurements. We then use the predict function to predict the species of new flowers with the given measurements.

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