# Dealing with Outliers¶

## Options for dealing with them:¶

1. Fix the data: Look at the data and correct it. Can be costly or impossible.
2. Censor: Delete observations that are outliers
3. Winsorize: Change the value so that it is closer to the rest of the distribution
• Example: Any value above the 99th percentile for a variable is changed to equal the 99th percentile
• This is a common and cheap ad-hoc correction that downplays the weight of the outlier in your analysis because the values are reduced, without tossing out the observation altogether
• Tough question that depends on the data/application: What is the "right" amount of the distribution to winsorize?

## Finding outliers¶

How can we find outliers?

1. Plot your data: scatterplot, hexplot, box plot, density, etc.
2. Compute z-scores and .describe() the data

Plotting is essential in EDA and data cleaning, as we've covered. I'm going to suggest the second route though as a quick and systematic way to identify which variables you should look into more.

Let's download our firm data (ccm).

In :
# copied from 3.3.4.1

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from io import BytesIO
from zipfile import ZipFile
from urllib.request import urlopen

url = 'https://github.com/LeDataSciFi/ledatascifi-2021/blob/main/data/CCM_cleaned_for_class.zip?raw=true'

# <-- that code would work, but GH said it was too big and
# forced me to zip it, so here is the work around to download it:

with urlopen(url) as request:

with ZipFile(data) as archive:
with archive.open(archive.namelist()) as stata:


And load a utility function from the community codebook.

In :
def outlier_report(df,vars_to_examine=None,color='red',thres=4,
return_df=False,no_print=False):
'''
Parameters
----------
df : DATAFRAME
Input dataframe
vars_to_examine : LIST, optional
List of variables to examine from dataframe. The default is df.columns.
color : STRING, optional
Color for cell highlighting. The default is 'red'.
thres : int, optional
Highlight cells where z score is above thres. The default is 4.
return_df : Boolean, optional
If true, will return the df obj (without styling) for further use.
The default is False.
no_print : Boolean, optional
If true, will not print.
The default is False.

Displays (if no_print=False)
-------
Table with distribution of z-scores of variables of interest.

Returns (if return_df=True)
-------
Table with distribution of z-scores of variables of interest (without styling).
'''

def highlight_extreme(s):
'''
Highlight extreme values in a series.
'''
is_extreme = abs(s) > thres
return ['background-color: '+color if v else '' for v in is_extreme]

if vars_to_examine==None:
vars_to_examine=df.columns

_tab = (
# compute z scores
((df[vars_to_examine] - df[vars_to_examine].mean())/df[vars_to_examine].std())
# output dist of z
.describe(percentiles=[.01,.05,.25,.5,.75,.95,.99]).T
# add a new column = highest of min and max column
.assign(max_z_abs = lambda x: x[['min','max']].abs().max(axis=1))
# now sort on it
.sort_values('max_z_abs',ascending = False)
)

if no_print == False:
display(_tab
.style.format('{:,.2f}')
.format({"count": '{:,.0f}'})
.apply(highlight_extreme,
subset=['mean', 'std', 'min', '1%', '5%', '25%', '50%', '75%', '95%','99%', 'max', 'max_z_abs'])
)

if return_df == True:
return _tab


Now we can pick the variables we want to check and use our utility function:

In :
vars_to_check = ['l_a', 'l_sale', 'prof_a', 'mb', 'ppe_a', 'capx_a', 'xrd_a',
'cash_a', 'div_d', 'td_a', 'td_mv', 'dltt_a', 'dv_a', 	'invopps_FG09',
'sales_g', 'short_debt', 'long_debt_dum', 'atr', 'smalltaxlosscarry',
'largetaxlosscarry', 'tnic3hhi', 'tnic3tsimm', 'prodmktfluid',
'delaycon', 'equitydelaycon', 'debtdelaycon', 'privdelaycon', 'l_emp',
'l_ppent', 'l_laborratio']

outlier_report(ccm,vars_to_check,thres=4)

count mean std min 1% 5% 25% 50% 75% 95% 99% max max_z_abs
dv_a 206,679 0.00 1.00 -0.12 -0.08 -0.08 -0.08 -0.08 -0.01 0.19 0.70 356.75 356.75
sales_g 196,652 -0.00 1.00 -4.75 -0.03 -0.02 -0.02 -0.01 -0.01 0.01 0.07 281.98 281.98
mb 219,269 0.00 1.00 -0.20 -0.15 -0.13 -0.10 -0.08 -0.01 0.30 0.96 272.32 272.32
invopps_FG09 193,956 0.00 1.00 -0.18 -0.15 -0.13 -0.10 -0.07 -0.00 0.29 0.91 261.27 261.27
dltt_a 222,002 0.00 1.00 -0.56 -0.56 -0.56 -0.53 -0.19 0.32 1.16 2.01 234.93 234.93
td_a 221,468 0.00 1.00 -0.78 -0.65 -0.65 -0.52 -0.13 0.33 1.10 1.85 199.83 199.83
prof_a 217,167 -0.00 1.00 -187.91 -0.96 -0.34 -0.03 0.04 0.10 0.20 0.32 171.16 187.91
xrd_a 223,001 -0.00 1.00 -2.60 -0.25 -0.25 -0.25 -0.25 -0.09 0.97 3.06 112.51 112.51
capx_a 206,399 0.00 1.00 -23.30 -0.71 -0.71 -0.54 -0.27 0.18 1.62 3.73 95.10 95.10
short_debt 194,560 0.00 1.00 -15.08 -0.98 -0.98 -0.82 -0.38 0.62 2.04 2.04 67.28 67.28
prodmktfluid 88,332 0.00 1.00 -1.91 -1.53 -1.28 -0.73 -0.18 0.55 1.84 2.97 8.52 8.52
l_laborratio 199,821 0.00 1.00 -6.40 -2.04 -1.36 -0.63 -0.13 0.48 1.91 2.98 7.57 7.57
tnic3tsimm 96,951 0.00 1.00 -0.51 -0.46 -0.45 -0.44 -0.38 -0.15 2.41 4.66 6.71 6.71
debtdelaycon 57,130 0.00 1.00 -3.09 -1.96 -1.47 -0.69 -0.11 0.60 1.81 2.72 5.99 5.99
l_emp 208,991 -0.00 1.00 -0.89 -0.89 -0.88 -0.76 -0.39 0.45 2.17 3.23 5.86 5.86
equitydelaycon 57,130 0.00 1.00 -2.94 -1.84 -1.43 -0.71 -0.11 0.58 1.87 2.82 5.28 5.28
privdelaycon 57,130 -0.00 1.00 -3.15 -1.93 -1.48 -0.70 -0.10 0.59 1.83 2.74 5.08 5.08
l_a 222,978 -0.00 1.00 -5.04 -2.00 -1.55 -0.73 -0.06 0.68 1.71 2.47 4.12 5.04
delaycon 57,130 0.00 1.00 -2.86 -1.92 -1.48 -0.72 -0.09 0.63 1.79 2.68 4.95 4.95
l_sale 218,779 0.00 1.00 -4.78 -2.63 -1.63 -0.63 -0.01 0.66 1.64 2.29 3.39 4.78
cash_a 222,332 -0.00 1.00 -1.12 -0.78 -0.77 -0.67 -0.42 0.25 2.36 3.61 4.10 4.10
l_ppent 218,212 -0.00 1.00 -1.46 -1.46 -1.37 -0.80 -0.14 0.66 1.87 2.59 3.81 3.81
tnic3hhi 96,951 0.00 1.00 -0.97 -0.92 -0.85 -0.67 -0.38 0.28 2.34 3.60 3.60 3.60
ppe_a 218,189 0.00 1.00 -1.09 -1.09 -1.06 -0.84 -0.29 0.58 2.08 2.53 2.89 2.89
td_mv 217,961 0.00 1.00 -1.25 -1.07 -1.07 -0.93 -0.25 0.70 1.95 2.47 2.75 2.75
smalltaxlosscarry 148,275 0.00 1.00 -0.46 -0.46 -0.46 -0.46 -0.46 -0.46 2.19 2.19 2.19 2.19
long_debt_dum 222,025 -0.00 1.00 -2.16 -2.16 -2.16 0.46 0.46 0.46 0.46 0.46 0.46 2.16
largetaxlosscarry 148,275 0.00 1.00 -0.59 -0.59 -0.59 -0.59 -0.59 1.69 1.69 1.69 1.69 1.69
atr 222,168 0.00 1.00 -1.48 -1.48 -1.48 -0.63 -0.36 1.33 1.33 1.33 1.33 1.48
div_d 206,688 0.00 1.00 -0.91 -0.91 -0.91 -0.91 -0.91 1.10 1.10 1.10 1.10 1.10

And you can extract a list of problematic variables from this function too:

In :
vars_with_big_outliers = list(outlier_report(ccm,vars_to_check,thres=4,return_df=True,no_print=True)
.query('max_z_abs > 5').index)


## Winsorizing¶

In this example:

1. If a value is below the 1st percentile, change it to the 1st percentile
2. If a value is above the 99th percentile, change it to the 99th percentile

Options:

1. Winsorize once over whole dataset
2. Winsorize over subgroups (e.g., winsorize by year)
• Useful when the distribution changes over time
• Suppose the distribution shifts right from one year to the next. If you winsorize both years at once, you'll chop off the lower values in year one and the upper values in year two. Perhaps it makes more sense to winsorize each year separately.

### Code:¶

from scipy.stats.mstats import winsorize

# option 1a:
for v in [some_list_of_vars]:
df[v] = winsorize(df[v],limits=[.01,.99])

# option 1b: same as 1a, but one line
df[some_list_of_vars]= df[some_list_of_vars].apply(lambda x: winsorize(x,limits=[.01,.99]))

# option 2: winsorize by group (e.g. year)
df[some_list_of_vars] = df.groupby(some_group)[some_list_of_vars].transform(lambda x: winsorize(x,limits=[.01,.99]))


### An example¶

In :
from scipy.stats.mstats import winsorize

practice_df = ccm.copy() # don't do this in your code,
# just run the remaining lines:

# winsorizse one var at a time
vars_to_win = vars_to_check # decide which, for this example - all the ones we checked
for v in vars_to_win:
practice_df[v] = winsorize(practice_df[v],limits=[.01,.99])


Let's verify it worked:

In :
(practice_df
.describe(percentiles=[.01,.05,.25,.5,.75,.95,.99]).T
# add a new column = highest of min and max column
.assign(abs_maxmin = lambda x: x[['min','max']].abs().max(axis=1))
# now sort on it
.sort_values('abs_maxmin',ascending = False)
[['min','1%',"99%",'max']] # only need these to see winsorizing in action
[10:15] # just print a few vars
.style.format('{:,.2f}')
)

Out:
min 1% 99% max
l_sale -1.64 -1.64 -1.64 -1.64
prof_a -1.05 -1.05 -1.05 -1.05
tnic3tsimm 1.01 1.01 1.01 1.01
sales_g -0.73 -0.73 -0.73 -0.73
mb 0.56 0.56 0.56 0.56