# Multinomial logistic regression With R

**R Statistics Blog**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

Multinomial logisticregression is used when the target variable is categorical with more than two levels. It is an extension of binomial logistic regression.

## Overview – Multinomial logistic Regression

Multinomial regression is used to predict the nominal target variable. In case the target variable is of ordinal type, then we need to use ordinal logistic regression. In this tutorial, we will see how we can run multinomial logistic regression. As part of data preparation, ensure that data is free of multicollinearity, outliers, and high influential leverage points.

## Case Study – What is UCI Breast Tissue?

In this tutorial, we will be using Breast Tissue data from UCI machine learning repository the classification of breast tissue. Originally, the breast tissues have been classified into 6 groups.

However, we will merge the fibro-adenoma, mastopathy, and glandular classes as their discrimination are not important. Check the tutorial on Dataframe Manipulations to learn about the merging of levels and other tasks related to dataframe in R programming.

## Reading the breast tissue data

library(readr) tissue <- read_csv("./static/data/BreastTissue.csv") # Checking the structure of adult data str(tissue)

# Output Classes ‘tbl_df’, ‘tbl’ and 'data.frame': 106 obs. of 11 variables: $ Case #: int 1 2 3 4 5 6 7 8 9 10 ... $ Class : chr "car" "car" "car" "car" ... $ I0 : num 525 330 552 380 363 ... $ PA500 : num 0.187 0.227 0.232 0.241 0.201 ... $ HFS : num 0.0321 0.2653 0.0635 0.2862 0.2443 ... $ DA : num 229 121 265 138 125 ... $ Area : num 6844 3163 11888 5402 3290 ... $ A/DA : num 29.9 26.1 44.9 39.2 26.3 ... $ Max IP: num 60.2 69.7 77.8 88.8 69.4 ... $ DR : num 220.7 99.1 253.8 105.2 103.9 ... $ P : num 557 400 657 494 425 ...

Combining levels of target variable and deleting the **case #** as it is a unique variable.

tissue <- tissue[, -1] tissue$Class <- as.factor(tissue$Class) levels(tissue$Class)[levels(tissue$Class) %in% c("fad", "gla", "mas")] <- "other" levels(tissue$Class)

# Output [1] "adi" "car" "con" "other"

## Building a Multinomial Regression Model

We will be predicting **Class** of the breast tissue using Breast Tissue data from the UCI machine learning repository.

### Splitting the data in train and test

#Splitting the data using a function from dplyr package library(caret) index <- createDataPartition(tissue$Class, p = .70, list = FALSE) train <- tissue[index,] test <- tissue[-index,]

### Setting the reference level

Unlike binary logistic regression in multinomial logistic regression, we need to define the reference level. Please note this is specific to the function which I am using from **nnet** package in R. There are some functions from other R packages where you don’t really need to mention the reference level before building the model.

# Setting the reference train$Class <- relevel(train$Class, ref = "adi")

### Training the multinomial classification model

To train the model, we will be using `multinom`

function from `nnet`

package. Once the model is trained, then we will use the summary() function to check the model coefficients.

require(nnet) # Training the multinomial model multinom_model <- multinom(Class ~ ., data = tissue) # Checking the model summary(multinom_model)

# Output Call: multinom(formula = Class ~ ., data = tissue) Coefficients: (Intercept) I0 PA500 HFS DA car 86.73299 -1.2415518 34.805551 -31.338876 -3.3819409 con 65.23130 -0.1313008 3.504613 5.178805 0.6902009 other 94.25666 -0.7356228 -9.929850 47.648766 -0.7567586 Area `A/DA` `Max IP` DR P car -0.01439290 -0.6831729 3.1996740 3.9293080 0.92505697 con -0.01189647 2.3845927 0.4270486 -0.1631782 -0.03680047 other -0.01590076 1.6362184 0.8789358 1.3702359 0.51944534 Std. Errors: (Intercept) I0 PA500 HFS car 0.038670563 0.11903866 0.019490301 0.0378583878 con 0.001741294 0.09413872 0.000350851 0.0005646109 other 0.038878992 0.11367934 0.019507244 0.0378385159 DA Area `A/DA` `Max IP` DR car 0.65220286 0.02077879 0.55684441 0.4874646 0.6119659 con 0.09834323 0.01535892 0.06383315 0.4114490 0.1080821 other 0.65428634 0.02068448 0.55666884 0.4881945 0.6102327 P car 0.1770202 con 0.1120580 other 0.1728985 Residual Deviance: 8.24364 AIC: 68.24364

Just like binary logistic regression, we need to convert the coefficients to odds by taking the exponential of the coefficients.

exp(coef(multinom_model))

The predicted values are saved as fitted.values in the model object. Let’s see the top 6 observations.

head(round(fitted(multinom_model), 2))

# Output adi car con other 1 0 0.97 0 0.03 2 0 1.00 0 0.00 3 0 1.00 0 0.00 4 0 1.00 0 0.00 5 0 1.00 0 0.00 6 0 0.97 0 0.03

The multinomial regression predicts the probability of a particular observation to be part of the said level. This is what we are seeing in the above table. Columns represent the classification levels and rows represent the observations. This means that the first six observation are classified as car.

### Predicting & Validating the model

To validate the model, we will be looking at the accuracy of the model. This accuracy can be calculated from the classification table.

# Predicting the values for train dataset train$ClassPredicted <- predict(multinom_model, newdata = train, "class") # Building classification table tab <- table(train$Class, train$ClassPredicted) # Calculating accuracy - sum of diagonal elements divided by total obs round((sum(diag(tab))/sum(tab))*100,2)

# Output [1] 98.68

*Our model accuracy has turned out to be 98.68% in the training dataset*.

### Predicting the class on test dataset.

# Predicting the class for test dataset test$ClassPredicted <- predict(multinom_model, newdata = test, "class") # Building classification table tab <- table(test$Class, test$ClassPredicted) tab

# Output adi car con other adi 6 0 0 0 car 0 6 0 0 con 0 0 4 0 other 0 0 0 14

*We were able to achieve 100% accuracy in the test dataset and this number is very close to train, and thus we conclude that the model is good and is also stable.*

In this tutorial, we learned how to build the multinomial logistic regression model, how to validate, and make a prediction on the unseen dataset.

**leave a comment**for the author, please follow the link and comment on their blog:

**R Statistics Blog**.

R-bloggers.com offers

**daily e-mail updates**about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.

Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.