pandas construct multi index for columns

Question

How can I construct a multi-index in pandas for an example dataframe of:

import pandas as pd
df = pd.DataFrame({'day':['2020-01-01', '2020-01-02'], 'value_mean':[1,5], 'value_max':[40,100]})

Transform the existing:

          day  value_mean  value_max
0  2020-01-01           1         40
1  2020-01-02           5        100

To something like:

                            value
          day         mean        max
0  2020-01-01           1         40
1  2020-01-02           5        100

Answer 1

There is problem join no Multiindex with MultiIndex columns, only trick should be use empty strings for second level:

df.columns = df.columns.str.split('_', expand=True)
df = df.rename(columns = lambda x: x if pd.notna(x) else '')
print (df)
          day value     
               mean  max
0  2020-01-01     1   40
1  2020-01-02     5  100

print (df.columns)
MultiIndex([(  'day',     ''),
            ('value', 'mean'),
            ('value',  'max')],
           )

If want clean, not empty strings values in levels:

df = df.set_index('day')
df.columns = df.columns.str.split('_', expand=True)
print (df)
           value     
            mean  max
day                  
2020-01-01     1   40
2020-01-02     5  100