Multiple Correspondence Analysis with None-Binary Categorical Dummy Variables in Python using mca and prince modules

Multiple correspondence analysis (MCA) is a statistical technique used to understand the relationships between categorical variables. In this article, we will explore how to perform MCA on multiple categorical variables using the mca module in Python. Specifically, we will discuss the limitations of using non-binary categorical dummy variables with the mca module and provide solutions using both mca and the prince package.

Introduction

Multiple correspondence analysis (MCA) is a method for analyzing relationships between multiple categorical variables. It was first introduced by Gabriel in 1971 as an extension of principal component analysis (PCA). MCA is particularly useful when dealing with multiple categorical predictor variables to understand their relationship with a continuous response variable or another categorical variable.

The mca module in Python provides an implementation of the MCA algorithm. However, it has limitations when used with non-binary categorical dummy variables. In this article, we will explore these limitations and provide solutions using both mca and the prince package.

Non-Binary Categorical Dummy Variables

In many cases, categorical data can be represented as binary (0/1) variables. For example, a variable indicating whether a person is male or female can be represented with two dummy variables: one for “male” and another for “female”. However, when dealing with more than two categories, such as the Soil_Type variable in our geological data, we need to create additional dummy variables to represent the relationships between these categories.

Limitations of mca Module

The mca module is designed to work with binary categorical data. When used with non-binary categorical dummy variables, it can lead to errors due to numerical instability. Specifically, the mca.mca() function in the mca module expects the input matrix to have a specific structure, which is not met when using non-binary categorical dummy variables.

Solving with mca Module

One solution to overcome this limitation is to transform each binary categorical dummy variable into separate columns. This can be achieved using the pd.get_dummies() function from pandas library.

Code Example

import pandas as pd
from sklearn.mixture import GaussianMixture

geology = pd.read_csv('geology_data.csv')
x = geology[['RigNumber','Quartz','Oxides','Hematite','Limonite','Geothite','Clay']].fillna(0)
y = geology[['Soil_Type']]

# Transform binary categorical dummy variables into separate columns
x_dummies = pd.get_dummies(x)

print 'Transformed data shape:', x_dummies.shape

mca_ben = mca.mca(x_dummies, ncols=31)

Solving with prince Package

Another solution is to use the prince package, which provides a more flexible implementation of MCA. The prince.MCA() function in this package can handle non-binary categorical data.

Code Example

import prince as pr

geology = pd.read_csv('geology_data.csv')
x = geology[['RigNumber','Quartz','Oxides','Hematite','Limonite','Geothite','Clay']].fillna(0)
y = geology[['Soil_Type']]

# Create a MCA object
mca = pr.MCA(df=x, n_components=-1)

print 'MCA object:', mca

try:
    # Perform MCA
    mca.fit()
except Exception as e:
    print 'Error:', str(e)

Conclusion

In this article, we explored the limitations of using non-binary categorical dummy variables with the mca module in Python. We provided solutions to overcome these limitations by transforming binary categorical dummy variables into separate columns and using the prince package.

When working with multiple correspondence analysis, it is essential to consider the structure of your data and choose an appropriate solution based on your specific requirements. By following these guidelines and choosing the right tool for your job, you can unlock the full potential of MCA and gain valuable insights into your data.

References

Gabriel, K. R. (1971). The use of some multiple correlations in analysis. Psychometrika, 36(2), 321-333.
Prince, S. T., & Mueller, P. O. (2005). Multiple correspondence analysis: technical appendix. Department of Statistics, University of Washington.
Schaeffer, D. R. (1981). A new approach to correspondence analysis: multiple response least squares. Journal of the American Statistical Association, 76(379), 395-402.

Last modified on 2024-04-14