co-relation with multiple categorical variables - statistics

Question

Is there a method to find a co-relation between multiple categorical variables? when you have a very big data set with a lot of categorical variables.

Answer 1

as #arpitrathi mentioned, typically you need to use Cramer's V.
AS I remember, there are already prepared code snippets on the internet,
I will leave you the one I am typically using for this, maybe it will help you.
You will need to import some libs to use it.
from scipy import stats
import seaborn as sns
import matplotlib.pyplot as plt
import pandas as pd
def cramers_v(x, y):
'''
Returns cramers_v for 2 categorical features
'''
confusion_matrix = pd.crosstab(x,y)
chi2 = stats.chi2_contingency(confusion_matrix)[0]
n = confusion_matrix.sum().sum()
phi2 = chi2/n
r,k = confusion_matrix.shape
phi2corr = max(0, phi2-((k-1)*(r-1))/(n-1))
rcorr = r-((r-1)**2)/(n-1)
kcorr = k-((k-1)**2)/(n-1)
return np.sqrt(phi2corr/min((kcorr-1),(rcorr-1)))
def heatmap_categorical_columns_w_dependant_categorical(df, dependent_variable, columns):
'''
Takes df, a dependant variable as str
Returns a heatmap of catecorical columns cramers_v with dependent variable
'''
plt.figure(figsize=(8, 10))
corrM = [cramers_v(df[dependent_variable], df[column]) for column in columns]
corr = pd.DataFrame(corrM, index=columns, columns=[dependent_variable])
ax = sns.heatmap(corr,
annot=True,
cmap='coolwarm',
vmin=-1,
vmax=1,
)
ax.set_title("Cramer V Correlation between Variables")
return ax
The result will be something like:
Example of usage you can check out in this code:
https://github.com/OzmundSedler/IBM-advanced-DS-coursera/blob/master/4%20Capstone%20/ML-project-draft.ipynb

Answer 2

You can use this code to get correlations among multiple variables using plt.matshow. Where 'bikesharing_data' is the pandas DataFrame.
plt.figure(figsize=[12, 8])
plt.matshow(bikesharing_data.corr(),
fignum=False,
aspect='equal')
columns = len(bikesharing_data.columns)
plt.xticks(range(columns), bikesharing_data.columns)
plt.yticks(range(columns), bikesharing_data.columns)
plt.colorbar()
plt.xticks(rotation=90)
plt.title('Correlation', y=1.2)
plt.show()
Where you can drop the numerical variables using:
features = bikesharing_data.drop(['x1', 'x2', ... ,'xn'], axis=1)
The resultant output is as follows;
Correlation Matrix