Correlation among multiple categorical variables (Pandas)

Question

I have a data set made of 22 categorical variables (non-ordered). I would like to visualize their correlation in a nice heatmap. Since the Pandas built-in function

DataFrame.corr(method='pearson', min_periods=1)

only implement correlation coefficients for numerical variables (Pearson, Kendall, Spearman), I have to aggregate it myself to perform a chi-square or something like it and I am not quite sure which function use to do it in one elegant step (rather than iterating through all the cat1*cat2 pairs). To be clear, this is what I would like to end up with (a dataframe):

         cat1  cat2  cat3  
  cat1|  coef  coef  coef  
  cat2|  coef  coef  coef
  cat3|  coef  coef  coef

Any ideas with pd.pivot_table or something in the same vein?

thanks in advance
D.

Asked By: zar3bski

||

Source

Answer 1

You can using pd.factorize

df.apply(lambda x : pd.factorize(x)[0]).corr(method='pearson', min_periods=1)
Out[32]: 
     a    c    d
a  1.0  1.0  1.0
c  1.0  1.0  1.0
d  1.0  1.0  1.0

Data input

df=pd.DataFrame({'a':['a','b','c'],'c':['a','b','c'],'d':['a','b','c']})

Update

from scipy.stats import chisquare

df=df.apply(lambda x : pd.factorize(x)[0])+1

pd.DataFrame([chisquare(df[x].values,f_exp=df.values.T,axis=1)[0] for x in df])

Out[123]: 
     0    1    2    3
0  0.0  0.0  0.0  0.0
1  0.0  0.0  0.0  0.0
2  0.0  0.0  0.0  0.0
3  0.0  0.0  0.0  0.0

df=pd.DataFrame({'a':['a','d','c'],'c':['a','b','c'],'d':['a','b','c'],'e':['a','b','c']})

Answered By: BENY

Answer 2

Turns out, the only solution I found is to iterate trough all the factor*factor pairs.

factors_paired = [(i,j) for i in df.columns.values for j in df.columns.values] 

chi2, p_values =[], []

for f in factors_paired:
    if f[0] != f[1]:
        chitest = chi2_contingency(pd.crosstab(df[f[0]], df[f[1]]))   
        chi2.append(chitest[0])
        p_values.append(chitest[1])
    else:      # for same factor pair
        chi2.append(0)
        p_values.append(0)

chi2 = np.array(chi2).reshape((23,23)) # shape it as a matrix
chi2 = pd.DataFrame(chi2, index=df.columns.values, columns=df.columns.values) # then a df for convenience

Answered By: zar3bski

Answer 3

Using association-metrics python package to calculate Cramér’s coefficient matrix from a pandas.DataFrame object it’s quite simple; let me show you:

First install association_metrics using:

pip install association-metrics

Then, you can use the following pseudocode

# Import association_metrics  
import association_metrics as am
# Convert you str columns to Category columns
df = df.apply(
        lambda x: x.astype("category") if x.dtype == "O" else x)

# Initialize a CamresV object using you pandas.DataFrame
cramersv = am.CramersV(df) 
# will return a pairwise matrix filled with Cramer's V, where columns and index are 
# the categorical variables of the passed pandas.DataFrame
cramersv.fit()

Answered By: Heber Trujillo

Correlation among multiple categorical variables (Pandas)

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