A Guide to Multivariate Logistic Regression

Often in business, it's important to be able to predict which actions could produce the most favorable outcomes. Multivariate logistic regression is a type of analysis that can help predict results when you're working with multiple variables. It's also a valuable calculation in machine learning programs. In this article, we explain what multivariate logistic regression is and how to create and evaluate models for it in Python.

What is multivariate logistic regression analysis?

Multivariate logistic regression analysis is a formula used to predict the relationships between dependent and independent variables. It calculates the probability of something happening depending on multiple sets of variables. This is a common classification algorithm used in data science and machine learning.

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Logistic vs. linear regression

There are two main forms of regression analysis. Linear regression has a continuous set of results that can easily be mapped on a graph as a straight line. For example, if you want to determine the likelihood that the number of books someone reads affects how much money they make, linear regression would be the best equation to use.

Logistic regressions are non-linear and are portrayed on a graph with a curved shape called a sigmoid. Instead of a continuous set of results, a logistical regression has two or more categories for data. If you want to learn the probability of getting a job based on how many applications you submit, whether you get a job is a discrete number of variables. Therefore, you would use a logistic regression program for that data.

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Types of logistic regression

Logistic regression includes three basic types:

• Binary: A binary output is a variable where there are only two possible outcomes. These outcomes must be opposite of each other and mutually exclusive. Whether you have a cat is a binary output.

• Multi-class: A multi-class has three or more categories without any numerical value, though they usually have a numerical stand-in for datasets. For example, you could ask if someone if they have a dog, cat or fish.

• Ordinal: An ordinal output also has three or more categories, though they're in a ranked output. For example, asking a friend if they like cats, dislike cats or don't care is an ordinal output.

Multivariable vs. multivariate logistic regression

While multivariable and multivariate regressions share similar functions and names, there is one key difference between them. In a multivariate regression, there are multiple independent variables and multiple outcomes. In multivariable regression, there are multiple independent variables, but only one outcome.

How to build and evaluate logistic regression models in Python

You can use multivariate logistic regression to create models in Python that may predict outcomes based on imported data. Here are the steps on how to build and evaluate a Python model using this regression:

1. Install the required packages

Python uses packages and libraries to run and carry out specific functions. In order to run a multivariate logistic regression, you need specific packages, including:

• Pandas for downloading, analyzing and editing data

• Numpy for performing numerical calculations

• Plotly for visualizing data and creating plots

You may also need Sklearn, Python's machine learning algorithm toolkit. Here are some of the tools inside of Sklearn:

• Linear_model for modeling the logistics regression model

• Metrics for calculating the accuracies once the model is trained

• Train_Test_Split for splitting the data into a training and testing data set

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2. Find a data set

In order to run a multivariate logistic regression, you need to have a set of data. The data requires more than one independent variable and two or more non-continuous outcomes. Once you find your data, download it into Python using the pandas package.

3. Clean and prepare the data

Once you download the data into Python, prepare the data for regression analysis. Remove rows and columns that don't have any data in them, as well as data values that you don't need for the regression analysis. After you have only the variables that you're working with, mark them as dependent or independent variables.

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4. Split the data

To understand the model's performance, split the data into two different datasets. One set is for training while the other for testing. Use the Sklearn tool test-train-split to split the data. You can choose which parameters to use in order to split the data, or divide it randomly. Determine how much of the information you need to use for each dataset. The most common ratio is 70% for model training and 30% for model testing.

5. Build the model

To build a model for the multivariate logistic regression, use the linear_model kit from Sklearn to import your variables. Run the "LogisticRegression" function to perform the regression. Fit your training data onto the model using the "fit" function and run the regression to train your model.

6. Evaluate the model

Evaluating your model is a key part of running logistic analysis since it allows you to make sure all of your variables are being measured accurately. One way to evaluate models is to use a confusion matrix. A confusion matrix is a table that checks a classification model's effectiveness by sorting the data into four categories:

• True Positive: Correctly predicts that an event happens

• True negative: Correctly predicts that an event doesn't happen

• False positive: Incorrectly predicts that an event happens

• False negative: Incorrectly predicts that an event doesn't happen

For example, your model predicts that teenage girls will watch a certain movie 10% of the time, but the data states they only watch it 5% of the time. A confusion matrix would flag that as a false positive.

7. Visualize the model

A confusion matrix can also be used to visualize your model with graphs and plots. Here are a few types of visualizations:

• A ROC curve: Compares the true positive rate and false positive rate in a data set.

• The area under the curve plot: Uses three confusion matrix metrics to analyze the general effectiveness of the model.

• A precision-recall tradeoff plot: Compares the precision of a model with its ability to recall results.

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