Is 'High School', 'Graduate', 'Unknown' ordinal or nominal data?

Question

My goal is to Feature Engineering the column Education_Level. This is an obvious ordinal data. However, I am having difficulty to put Education_Level to choose -1 or np.nan. The difficulty is that I don't know the effect of np.nan and -1 to the regression, classification, clustering algorithm.

I believe the ordinal level as follow: 1 = 'Uneducated', 2 = 'High School', 3 = 'College', 4 = 'Graduate', 5 = 'Post-Graduate', 6 = 'Doctorate'

df['Education_Leve'].value_counts()

Graduate         3128
High School      2013
Unknown          1519
Uneducated       1487
College          1013
Post-Graduate     516
Doctorate         451

What I've did:

1. I tried to simulate it with the scikit-learn library.

ord_enc = OrdinalEncoder(categories=[
    ['Uneducated', 'High School', 'College', 'Graduate', 'Post-Graduate', 'Doctorate']
], handle_unknown='use_encoded_value', unknown_value=np.nan).fit(df)
X_encoded = ord_enc.transform(X=df)
sca = MinMaxScaler().fit(X=X_encoded)
X_scaled = sca.transform(X=X_encoded)
X_scaled

X_scaled (with unknown_value=np.nan)

array([[0.6],
       [0.2],
       [nan],
       [0. ],
       [0.4],
       [0.8],
       [1. ]])

X_scaled (with unknown_value=-1)

array([[0.66666667],
       [0.33333333],
       [0.        ],
       [0.16666667],
       [0.5       ],
       [0.83333333],
       [1.        ]])

What I know is that: unknown_value=-1 will affect the scaler, while unknown_value=np.nan should not. My assumption is that in a Linear Regression where we have equation ie y = ax + b, if X is np.nan, it will become y = b while if X is -1, it will become y = -1 + b.

By the time I write this post, I believe the answer is 'It depends'.

1. It is ordinal if you believe that the higher the education level, the less likely a person will churn.
2. If you believe there is no order of churn ('Graduate' > 'High School' < 'Uneducated'. ie 'Graduate' is more likely to churn than 'High School' but less likely to churn than 'Uneducated'). Then you can't use ordinal. With ordinal, you only have 1-axis, while with nominal, you have 6-axis.
3. It is nominal if you believe (it depends on specific education level) if a person is going to churn or not.

Answer 1

The variable Eduction with levels 'Uneducated', 'High School', 'College', 'Graduate', 'Post-Graduate' and 'Doctorate' is certainly an ordered categorical variable. Indeed, we all agree that these levels can be ordered in a meaningful way.

A legitimate question may be: is the distance between Uneducated and High School the same as the distance between Post-Graduate and Doctorate? The answer to this question is, I guess, opinion-based.

If you included a further level 'Unknown' then this would destroy

we all agree that these levels can be ordered in a meaningful way

Since there is no meaningful where to place Unknown in the ordered list. In my opinion, 'Unknown' is most likely missing information and thus it cannot be treated as level.

Answer 2

Education level is ordinal, as you already noticed. However, you cannot consider "Unknown" as one of the ordinal levels, it is missing data, so what you need to do is pick one of many approaches to deal with missing-data.

As an additional comment, OrdinalEncoder from scikit-learn encodes the levels as integers and this is not necessarily the best encoding. With ordinal data, we assume that there is ordering between the categories, the values do not have standard numerical interpretation (you cannot subtract them, etc) as we can do with interval or ratio data. When you use such coding, you are ignoring the fact that the variable is ordinal and treat the categories as if they had a numerical meaning.