Issue
I have a DataFrame, df
, with a non-numerical column CatColumn
.
A B CatColumn
0 381.1396 7.343921 Medium
1 481.3268 6.786945 Medium
2 263.3766 7.628746 High
3 177.2400 5.225647 Medium-High
I want to include CatColumn
in the correlation analysis with other columns in the Dataframe. I tried DataFrame.corr
but it does not include columns with nominal values in the correlation analysis.
Solution
I am going to strongly disagree with the other comments.
They miss the main point of correlation: How much does variable 1 increase or decrease as variable 2 increases or decreases. So in the very first place, order of the ordinal variable must be preserved during factorization/encoding. If you alter the order of variables, correlation will change completely. If you are building a tree-based method, this is a non-issue but for a correlation analysis, special attention must be paid to preservation of order in an ordinal variable.
Let me make my argument reproducible. A and B are numeric, C is ordinal categorical in the following table, which is intentionally slightly altered from the one in the question.
rawText = StringIO("""
A B C
0 100.1396 1.343921 Medium
1 105.3268 1.786945 Medium
2 200.3766 9.628746 High
3 150.2400 4.225647 Medium-High
""")
myData = pd.read_csv(rawText, sep = "\s+")
Notice: As C moves from Medium to Medium-High to High, both A and B increase monotonically. Hence we should see strong correlations between tuples (C,A) and (C,B). Let's reproduce the two proposed answers:
In[226]: myData.assign(C=myData.C.astype('category').cat.codes).corr()
Out[226]:
A B C
A 1.000000 0.986493 -0.438466
B 0.986493 1.000000 -0.579650
C -0.438466 -0.579650 1.000000
Wait... What? Negative correlations? How come? Something is definitely not right. So what is going on?
What is going on is that C is factorized according to the alphanumerical sorting of its values. [High, Medium, Medium-High] are assigned [0, 1, 2], therefore the ordering is altered: 0 < 1 < 2 implies High < Medium < Medium-High, which is not true. Hence we accidentally calculated the response of A and B as C goes from High to Medium to Medium-High. The correct answer must preserve ordering, and assign [2, 0, 1] to [High, Medium, Medium-High]. Here is how:
In[227]: myData['C'] = myData['C'].astype('category')
myData['C'].cat.categories = [2,0,1]
myData['C'] = myData['C'].astype('float')
myData.corr()
Out[227]:
A B C
A 1.000000 0.986493 0.998874
B 0.986493 1.000000 0.982982
C 0.998874 0.982982 1.000000
Much better!
Note1: If you want to treat your variable as a nominal variable, you can look at things like contingency tables, Cramer's V and the like; or group the continuous variable by the nominal categories etc. I don't think it would be right, though.
Note2: If you had another category called Low, my answer could be criticized due to the fact that I assigned equally spaced numbers to unequally spaced categories. You could make the argument that one should assign [2, 1, 1.5, 0] to [High, Medium, Medium-High, Small], which would be valid. I believe this is what people call the art part of data science.
Answered By - FatihAkici
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