# Multinomial Logistic Regression

## Introduction

Multinomial logistic regression model is a statistical model with an assumption that linear relationships are there between explanatory variable and a response variable of multiple labels.

## How to Access?

There are two ways to access. One is to access from 'Add' (Plus) button.

![](https://2850417076-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M4HLCK3olgduYoe3RVS%2F-M4oMvCUDQwHTJ0eWi_f%2F-M4oNHQUJ1nQvxEFJPYW%2Fmultinom_add.png?generation=1586795490786783\&alt=media)

Another way is to access from a column header menu from a numeric column.

![](https://2850417076-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M4HLCK3olgduYoe3RVS%2F-M4oMvCUDQwHTJ0eWi_f%2F-M4oNHQ_6YOOquSuFGpq%2Fmultinom_cols.png?generation=1586795491507107\&alt=media)

## How to Use?

### Column Selection

There are two ways to set what you want to predict by what variables.

![](https://2850417076-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M4HLCK3olgduYoe3RVS%2F-M4oMvCUDQwHTJ0eWi_f%2F-M4oNHQd0wFMwsAN332J%2Fmultinom_select.png?generation=1586795491021806\&alt=media)

If you are on "Select Columns" tab, you can set them by column selector.

![](https://2850417076-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M4HLCK3olgduYoe3RVS%2F-M4oMvCUDQwHTJ0eWi_f%2F-M4oNHQgjc5o9RqibGCT%2Fmultinom_custom.png?generation=1586795491600515\&alt=media)

If you are on "Custom" tab, you can type a formula directly.

### Train Test Split

![](https://2850417076-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M4HLCK3olgduYoe3RVS%2F-M4oMvCUDQwHTJ0eWi_f%2F-M4oNHQjAy49hkYrqC82%2Fmultinom_split.png?generation=1586795490946079\&alt=media)

You can split the data into training and test to evaluate the performance of the model. You can set

* Test Data Set Ratio - Ratio of test data in the whole data.
* Random Seed to Split Training/Test - You can change random seed to try other training and test data combination.

### Parameters

* A Vector to Subset Data (Optional) - "subset" parameter of lm function.
* Weight Vector (Optional) - "weights" parameter of lm function.
* How to treat NA? (Optional) - "na.action" parameter of lm. function. The default is "na.fail". This changes the behaviour of NA data. Can be one of the following.
  * "na.omit"
  * "na.fail"
  * "na.exclude"
  * "na.pass"
  * NULL
* Return Hessian Object? (Optional) - "Hess" parameter of multinom function. The default is FALSE. Whether the Hessian (the observed/expected information matrix) should be returned.
* How to summarize duplicate rows? (Optional) - "summ" parameter of multinom function. The default is no summarize. If this is indicated, summarize by deleting duplicate rows and adjust weights. Methods 1 and 2 differ in speed (2 uses C); method 3 also combines rows with the same X and different Y, which changes the baseline for the deviance.
* Censored (Optional) - "censored" parameter of multinom function. The default is TRUE. If Y is a matrix with K columns, interpret the entries as one for possible classes, zero for impossible classes, rather than as counts.
* Return Model Object (Optional) - "model" parameter of multinom function. The default is TRUE. If TRUE, the model frame is saved as component model of the returned object.

## How to Read Summary

![](https://2850417076-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M4HLCK3olgduYoe3RVS%2F-M4oMvCUDQwHTJ0eWi_f%2F-M4oNHQnikZSOkWtra8o%2Fmultinom_summary.png?generation=1586795491282938\&alt=media)

Once you run it, you will see summary info like this.

### Summary of Fit

* Effective Number of DF - Effective number of degree of freedom.
* Deviance - The residual deviance, compared to the full saturated model (that explains individual observations exactly). Also, minus twice log-likelihood.
* AIC - The AIC for this fit.
* Base Level of \~ - Base line value of factor variables. The values in Parameter Estimates are relative values compared to these base levels

### Parameter Estimates

* Predicted Label - Labels of response variable.
* Term - The term in the model being estimated and tested.
* Estimate - The estimated coefficient.
* Std Error - The standard error from the linear model.
* t Ratio - t-statistic.
* P Value - Two sided p-value.
* Conf Low - Lower bound of 95% confidence interval.
* Conf High - Upper bound of confidence interval.
* Odds Ratio - Exponent of the estimated coefficient.

## Step-by-step

Here's a step-by-step tutorial guide on how you can build, predict and evaluate multinomial logistic regression model.

<https://blog.exploratory.io/exploratory-v3-1-released-62e7a2974d4b#487d>