Pandas¶

  • https://pandas.pydata.org
  • very high-level data containers with corresponding functionality
  • many useful tools to work with time-series (look at Series.rolling)
  • many SQL-like data operations (group, join, merge)
  • Interface to a large variety of file formats (see pd.read_[...] functions)
  • additional package with data-interface/API to many data repositories (https://pandas-datareader.readthedocs.io/en/latest/remote_data.html)
In [1]:
import pandas as pd

Basic Data Structures¶

Series¶

One-dimensional ndarray with axis labels (called index).

Series can be created like an array

In [2]:
pd.Series([11,13,17,19,23])
Out[2]:
0    11
1    13
2    17
3    19
4    23
dtype: int64

or, if you want a special index

In [3]:
series = pd.Series([11,13,17,19,23], index=['a', 'b', 'c', 'd', 'e'])
print(series)

a    11
b    13
c    17
d    19
e    23
dtype: int64

to get the content back you can use

In [4]:
series.index
Out[4]:
Index(['a', 'b', 'c', 'd', 'e'], dtype='object')
In [5]:
series.values
Out[5]:
array([11, 13, 17, 19, 23])

but the power of pandas lies in all the other attributes

In [6]:
#series. [TAB]

DataFrame¶

The primary pandas data structure.

Two-dimensional size-mutable, potentially heterogeneous tabular data structure with labeled axes. (index: row labels, columns: column labels) Can be thought of as a dict-like container for Series objects.

The easiest way to create a DataFrame is to read it from an input file (see later)

In addition there are many ways to create DataFrames manually. Most straight forward probably is to use a dict of iterables. (Series, Lists, Arrays). Pandas tries to choose sensible indexes.

In [7]:
frame = pd.DataFrame({"primes": series, "fibo": [1,1,2,3,5], "0-4": range(5)})
In [8]:
print(frame)

   primes  fibo  0-4
a      11     1    0
b      13     1    1
c      17     2    2
d      19     3    3
e      23     5    4

Refugee Example¶

We now want to use pandas to work with data from the World Bank. My goal is to create a plot showing the burden refugees put on different countries. For this we will plot the fraction of refugee in a give countries population versus that countries GDP.

I downloaded and extracted the following data-sets from the Worldbank website manually:

  • Refugee population by country or territory of asylum: https://data.worldbank.org/indicator/SM.POP.REFG
  • Population, total: https://data.worldbank.org/indicator/SP.POP.TOTL
  • GDP per capita (current US$): https://data.worldbank.org/indicator/NY.GDP.PCAP.CD
In [9]:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

Loading and Accessing Data¶

loading a data file with pandas is trivial

In [10]:
refugees = pd.read_csv("data/refugee-population.csv", skiprows=4)
In [11]:
refugees.head()
Out[11]:
Country Name Country Code Indicator Name Indicator Code 1960 1961 1962 1963 1964 1965 ... 2011 2012 2013 2014 2015 2016 2017 2018 2019 Unnamed: 64
0 Aruba ABW Refugee population by country or territory of ... SM.POP.REFG NaN NaN NaN NaN NaN NaN ... NaN NaN 1.0 NaN 2.0 1.0 NaN NaN NaN NaN
1 Afghanistan AFG Refugee population by country or territory of ... SM.POP.REFG NaN NaN NaN NaN NaN NaN ... 3009.0 16187.0 16863.0 300423.0 257554.0 59771.0 75927.0 72231.0 NaN NaN
2 Angola AGO Refugee population by country or territory of ... SM.POP.REFG NaN NaN NaN NaN NaN NaN ... 16223.0 23413.0 23783.0 15474.0 15555.0 15555.0 41109.0 39865.0 NaN NaN
3 Albania ALB Refugee population by country or territory of ... SM.POP.REFG NaN NaN NaN NaN NaN NaN ... 82.0 86.0 93.0 104.0 104.0 138.0 89.0 131.0 NaN NaN
4 Andorra AND Refugee population by country or territory of ... SM.POP.REFG NaN NaN NaN NaN NaN NaN ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN

5 rows × 65 columns

As you can see pandas choose the right column labels and numbered the rows continously.

We can easily change the row labels (the index) to one of the columns.

In [12]:
refugees.set_index(["Country Code"], inplace=True)
In [13]:
refugees.head()
Out[13]:
Country Name Indicator Name Indicator Code 1960 1961 1962 1963 1964 1965 1966 ... 2011 2012 2013 2014 2015 2016 2017 2018 2019 Unnamed: 64
Country Code
ABW Aruba Refugee population by country or territory of ... SM.POP.REFG NaN NaN NaN NaN NaN NaN NaN ... NaN NaN 1.0 NaN 2.0 1.0 NaN NaN NaN NaN
AFG Afghanistan Refugee population by country or territory of ... SM.POP.REFG NaN NaN NaN NaN NaN NaN NaN ... 3009.0 16187.0 16863.0 300423.0 257554.0 59771.0 75927.0 72231.0 NaN NaN
AGO Angola Refugee population by country or territory of ... SM.POP.REFG NaN NaN NaN NaN NaN NaN NaN ... 16223.0 23413.0 23783.0 15474.0 15555.0 15555.0 41109.0 39865.0 NaN NaN
ALB Albania Refugee population by country or territory of ... SM.POP.REFG NaN NaN NaN NaN NaN NaN NaN ... 82.0 86.0 93.0 104.0 104.0 138.0 89.0 131.0 NaN NaN
AND Andorra Refugee population by country or territory of ... SM.POP.REFG NaN NaN NaN NaN NaN NaN NaN ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN

5 rows × 64 columns

Now it's easy to select rows or columns

In [14]:
refugees.loc[["CHE","DEU"]]
Out[14]:
Country Name Indicator Name Indicator Code 1960 1961 1962 1963 1964 1965 1966 ... 2011 2012 2013 2014 2015 2016 2017 2018 2019 Unnamed: 64
Country Code
CHE Switzerland Refugee population by country or territory of ... SM.POP.REFG NaN NaN NaN NaN NaN NaN NaN ... 50416.0 50747.0 52464.0 62620.0 73336.0 82681.0 92995.0 104037.0 NaN NaN
DEU Germany Refugee population by country or territory of ... SM.POP.REFG NaN NaN NaN NaN NaN NaN NaN ... 571684.0 589737.0 187567.0 216973.0 316115.0 669482.0 970302.0 1063837.0 NaN NaN

2 rows × 64 columns

In [15]:
refugees[["1990","2000"]].head()
Out[15]:
1990 2000
Country Code
ABW NaN NaN
AFG 50.0 NaN
AGO 11557.0 12086.0
ALB NaN 523.0
AND NaN NaN
In [16]:
refugees.get(["1990","2000"]).head()
Out[16]:
1990 2000
Country Code
ABW NaN NaN
AFG 50.0 NaN
AGO 11557.0 12086.0
ALB NaN 523.0
AND NaN NaN

Working with a Single Country¶

With this we now choose the data for one country, remove all missing values and then create a plot:

In [17]:
che = refugees.loc["CHE"][[str(year) for year in range(1990,2020)]]
In [18]:
che.dropna().plot()
plt.show()

Usually it is easier to work with real datetime objects instead of strings. So we convert the index to datetime

In [19]:
che.index.values
Out[19]:
array(['1990', '1991', '1992', '1993', '1994', '1995', '1996', '1997',
       '1998', '1999', '2000', '2001', '2002', '2003', '2004', '2005',
       '2006', '2007', '2008', '2009', '2010', '2011', '2012', '2013',
       '2014', '2015', '2016', '2017', '2018', '2019'], dtype=object)
In [20]:
che.index = pd.to_datetime(che.index, format="%Y")
print(che.index)

DatetimeIndex(['1990-01-01', '1991-01-01', '1992-01-01', '1993-01-01',
               '1994-01-01', '1995-01-01', '1996-01-01', '1997-01-01',
               '1998-01-01', '1999-01-01', '2000-01-01', '2001-01-01',
               '2002-01-01', '2003-01-01', '2004-01-01', '2005-01-01',
               '2006-01-01', '2007-01-01', '2008-01-01', '2009-01-01',
               '2010-01-01', '2011-01-01', '2012-01-01', '2013-01-01',
               '2014-01-01', '2015-01-01', '2016-01-01', '2017-01-01',
               '2018-01-01', '2019-01-01'],
              dtype='datetime64[ns]', freq=None)

As mentioned in the introduction, pandas offers a very usefull rolling method

In [21]:
che.plot()
che.rolling(center=False,window=5).mean().plot()
plt.show()

Removing Unwanted Data¶

We now want to create a scatter plot with refugees divided by gdp vs. gdp-per-captita. For each data set we will use the mean of the last 7 years.

Some of the rows and columns in the World-Bank Files are of no interest for this. We can remove these easily.

Excluding Non-Countries¶

The World-Bank provides meta-data for each country, where we can identify rows with non-countries (e.g. regional aggregates)

In [22]:
!head data/metadata-countries_population.csv

We load this file and extract the two relevant columns

In [23]:
meta = pd.read_csv("data/metadata-countries_population.csv")
In [24]:
meta.columns
Out[24]:
Index(['Country Code', 'Region', 'IncomeGroup', 'SpecialNotes', 'TableName',
       'Unnamed: 5'],
      dtype='object')
In [25]:
meta = meta[['Country Code', 'Region']]
In [26]:
meta.head()
Out[26]:
Country Code Region
0 ABW Latin America & Caribbean
1 AFG South Asia
2 AGO Sub-Saharan Africa
3 ALB Europe & Central Asia
4 AND Europe & Central Asia
In [27]:
meta.set_index("Country Code", inplace=True)

From this we create a list of non-countries

In [28]:
non_countries = meta.loc[meta.Region.isnull()].index
print(non_countries)

Index(['ARB', 'CEB', 'CSS', 'EAP', 'EAR', 'EAS', 'ECA', 'ECS', 'EMU', 'EUU',
       'FCS', 'HIC', 'HPC', 'IBD', 'IBT', 'IDA', 'IDB', 'IDX', 'LAC', 'LCN',
       'LDC', 'LIC', 'LMC', 'LMY', 'LTE', 'MEA', 'MIC', 'MNA', 'NAC', 'OED',
       'OSS', 'PRE', 'PSS', 'PST', 'SAS', 'SSA', 'SSF', 'SST', 'TEA', 'TEC',
       'TLA', 'TMN', 'TSA', 'TSS', 'UMC', 'WLD'],
      dtype='object', name='Country Code')

and finally exclude the relevant rows

In [29]:
refugees = refugees.drop(non_countries)

Excluding Columns¶

The data contains a few rows with unneeded text

In [30]:
refugees.columns
Out[30]:
Index(['Country Name', 'Indicator Name', 'Indicator Code', '1960', '1961',
       '1962', '1963', '1964', '1965', '1966', '1967', '1968', '1969', '1970',
       '1971', '1972', '1973', '1974', '1975', '1976', '1977', '1978', '1979',
       '1980', '1981', '1982', '1983', '1984', '1985', '1986', '1987', '1988',
       '1989', '1990', '1991', '1992', '1993', '1994', '1995', '1996', '1997',
       '1998', '1999', '2000', '2001', '2002', '2003', '2004', '2005', '2006',
       '2007', '2008', '2009', '2010', '2011', '2012', '2013', '2014', '2015',
       '2016', '2017', '2018', '2019', 'Unnamed: 64'],
      dtype='object')

In addition, the 2019 column is empty

In [31]:
np.any(refugees["2019"].notnull())
Out[31]:
False

so we can create a list of all interesting columns

In [32]:
useful_cols = []
for year in range(2010,2019):
    useful_cols.append(str(year))
In [33]:
useful_cols
Out[33]:
['2010', '2011', '2012', '2013', '2014', '2015', '2016', '2017', '2018']

with this, we:

  • select the reduced datase
  • switch the index to Country Code
  • calculate the mean for each country
In [34]:
refugees = refugees[useful_cols]
In [35]:
refugee_means = refugees.mean(axis=1)

Loading Additional Files¶

Of course we could execute these commands again manually for the two remaining data-files. However, the proper way to solve this is to create a function for this. Especially since all files have the exact same structure.

In [36]:
def load_file(file):
    """Load and process a Worldbank File"""
    data = pd.read_csv(file, skiprows=4)
    data.set_index("Country Code", inplace=True)
    data.drop(non_countries, inplace=True)
    data = data[[str(year) for year in range(2010,2017)]]
    return data.mean(axis=1), data
In [37]:
gdp_means, gdp = load_file("data/gdp-per-capita.csv")
In [38]:
gdp_means.head()
Out[38]:
Country Code
ABW    24972.420561
AFG      593.293323
AGO     4519.970434
ALB     4263.977328
AND    39345.839439
dtype: float64
In [39]:
gdp.head()
Out[39]:
2010 2011 2012 2013 2014 2015 2016
Country Code
ABW 23512.602596 24985.993281 24713.698045 25025.099563 25533.569780 25796.380251 25239.600411
AFG 543.303042 591.162346 641.872034 637.165044 613.856333 578.466353 547.228110
AGO 3587.883798 4615.468028 5100.095808 5254.882338 5408.410496 4166.979684 3506.072885
ALB 4094.362119 4437.178067 4247.614279 4413.081743 4578.666720 3952.829458 4124.108907
AND 39736.354063 41100.729938 38392.943901 40626.751632 42300.334128 36039.653496 37224.108916
In [40]:
population_means, population = load_file("data/population.csv")

Creating the Plot¶

We now combine our three Series with means into one DataFrame and create our plot.

In [41]:
data = pd.DataFrame({"gdp": gdp_means, "refugees": refugee_means/population_means}).dropna()

(Here we loose some countries with missing data.)

In [42]:
data.plot.scatter("gdp", "refugees")
plt.show()

We can quickly find out who the three top countries are:

In [43]:
data.where(data["refugees"]>0.1).dropna()
Out[43]:
gdp refugees
Country Code
JOR 3951.958197 0.317788
LBN 7766.668886 0.194719
PSE 2861.802636 0.508273

To improve readability:

  • we switch to a log-log axis (we need to exclude countries with too small refugee numbers)
  • we highlight one selected country
  • We add a title
In [44]:
ax = data[data["refugees"] > 1e-10].plot.scatter(y="refugees", x="gdp", loglog=True)
ax = data.loc[["CHE"]].plot.scatter(y="refugees", x="gdp", ax=ax, color="r", label="Switzerland")
plt.title("refugees fraction vs. gdp")
plt.show()

again we can print the info for one country

In [45]:
data.loc["CHE"]
Out[45]:
gdp         82933.055377
refugees        0.008484
Name: CHE, dtype: float64

Highlighting a Full Region¶

Based on th meta data provided by the World Bank, we can highlight a region

In [46]:
europe = meta.loc[meta.Region == "Europe & Central Asia"].index
In [47]:
europe[:10]
Out[47]:
Index(['ALB', 'AND', 'ARM', 'AUT', 'AZE', 'BEL', 'BGR', 'BIH', 'BLR', 'CHE'], dtype='object', name='Country Code')
In [48]:
ax = data[data["refugees"] > 1e-10].plot.scatter(y="refugees", x="gdp", loglog=True)
ax = data.loc[data.index.intersection(europe)].plot.scatter(y="refugees", x="gdp", ax=ax, color="r", label="Europe & Central Asia")
plt.title("refugees fraction vs. gdp")
plt.show()

(As we lost some countries with missing data when we called dropna above, we need the data.index.intersection-call to select only country codes really contained in our data.)

Fitting¶

We now look at a tiny subset of this data and look at ways to fit a function to it.

Scipy preparse a huge number of options, we will look at three options of increasing complexity and flexibility.

Preparations¶

first we select our subset

In [49]:
europe_small = ['AUT',
 'DEU',
 'FRA',
 'ITA',
]
In [50]:
data_eu = data.loc[europe_small].dropna()
In [51]:
ax = data_eu.plot.scatter(y="refugees", x="gdp", color="r")
plt.title("refugees fraction vs. gdp")
plt.show()

and we create a vector with all the x values we will need to plot our fit result

In [52]:
x = np.linspace(data_eu["gdp"].min(), data_eu["gdp"].max(), 100)

polyfit¶

Polyfit is probably the easiest way to fit a polynome to given data.

In [53]:
from numpy import polyfit, polyval
In [54]:
res = polyfit(data_eu["gdp"], data_eu["refugees"],1)
print(res)

[ 5.20472464e-07 -1.64261467e-02]
In [55]:
ax = data_eu.plot.scatter(y="refugees", x="gdp", color="r")
ax.plot(x, polyval(res, x))
plt.title("refugees fraction vs. gdp")
plt.show()

curve_fit¶

With curve_fit you can define a complex fit function.

In [56]:
from scipy.optimize import curve_fit
In [57]:
def fit_function(x,b,c):
    return b*x+c
In [58]:
res = curve_fit(fit_function, data_eu["gdp"], data_eu["refugees"])
print(res)

(array([ 5.20472463e-07, -1.64261467e-02]), array([[ 3.86848840e-15, -1.62289029e-10],
       [-1.62289029e-10,  6.90771771e-06]]))
In [59]:
ax = data_eu.plot.scatter(y="refugees", x="gdp", color="r")
ax.plot(x, fit_function(x, *(res[0])))
plt.title("refugees fraction vs. gdp")
plt.show()

leastsq¶

Finally, least-squares allows you to even specify the cost function. With this you can factor in uncertainties or weights for your data points.

In [60]:
from scipy.optimize import leastsq
In [61]:
def fit_function(x, p):
    return x*p[0]+p[1]
In [62]:
def error_function(params):
    return data_eu["refugees"] - fit_function(data_eu["gdp"], params)
In [63]:
res = leastsq(error_function, [0,0])
print(res)

(array([ 5.20472464e-07, -1.64261467e-02]), 3)
In [64]:
ax = data_eu.plot.scatter(y="refugees", x="gdp", color="r")
ax.plot(x, fit_function(x, res[0]))
plt.title("refugees fraction vs. gdp")
plt.show()

statsmodels¶

In [65]:
import statsmodels.formula.api as smf
In [66]:
res = smf.ols("refugees ~ gdp", data=data_eu).fit()
In [67]:
print(res.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:               refugees   R-squared:                       0.972
Model:                            OLS   Adj. R-squared:                  0.958
Method:                 Least Squares   F-statistic:                     70.03
Date:                Tue, 12 Jul 2022   Prob (F-statistic):             0.0140
Time:                        07:41:11   Log-Likelihood:                 25.185
No. Observations:                   4   AIC:                            -46.37
Df Residuals:                       2   BIC:                            -47.60
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept     -0.0164      0.003     -6.250      0.025      -0.028      -0.005
gdp         5.205e-07   6.22e-08      8.368      0.014    2.53e-07    7.88e-07
==============================================================================
Omnibus:                          nan   Durbin-Watson:                   3.279
Prob(Omnibus):                    nan   Jarque-Bera (JB):                0.402
Skew:                          -0.551   Prob(JB):                        0.818
Kurtosis:                       1.905   Cond. No.                     3.52e+05
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 3.52e+05. This might indicate that there are
strong multicollinearity or other numerical problems.

/usr/lib/python3/dist-packages/statsmodels/stats/stattools.py:74: ValueWarning: omni_normtest is not valid with less than 8 observations; 4 samples were given.
  warn("omni_normtest is not valid with less than 8 observations; %i "
In [68]:
print(res.params)

Intercept   -1.642615e-02
gdp          5.204725e-07
dtype: float64
In [69]:
ax = data_eu.plot.scatter(y="refugees", x="gdp", color="r")
ax.plot(x, res.params[1]*x+res.params[0])
plt.title("refugees fraction vs. gdp")
plt.show()

Appendix: Selecting from DataFrames¶

Accessing Rows¶

Passing a single value to loc returns a Series

In [70]:
frame.loc["a"]
Out[70]:
primes    11
fibo       1
0-4        0
Name: a, dtype: int64

Passing a list to loc returns a DataFrame (even if the list contains a single a single value)

In [71]:
frame.loc[["a"]]
Out[71]:
primes fibo 0-4
a 11 1 0
In [72]:
frame.loc[["a","c"]]
Out[72]:
primes fibo 0-4
a 11 1 0
c 17 2 2

Also slicing works (but includes the upper boundary)

In [73]:
frame.loc["b":"d"]
Out[73]:
primes fibo 0-4
b 13 1 1
c 17 2 2
d 19 3 3

A list of boolean values with n-Rows entries, is considered a mask to select rows

In [74]:
frame.loc[[True,False,True,False,True]]
Out[74]:
primes fibo 0-4
a 11 1 0
c 17 2 2
e 23 5 4

Instead of a list, a boolean-series can be used. Rows are matched on the index. (frame[["primes"]] > 20 would not work as this returns a frame instead of a series.)

In [75]:
frame.loc[frame["primes"] > 20]
Out[75]:
primes fibo 0-4
e 23 5 4

When using a mask, .loc is optional (but recommended to avoid confusion with columns).

In [76]:
frame[frame["primes"] > 20]
Out[76]:
primes fibo 0-4
e 23 5 4

Using iloc it is possible to access rows by position as well. (without using the index)

In [77]:
frame.iloc[2:-1]
Out[77]:
primes fibo 0-4
c 17 2 2
d 19 3 3

Accessing Columns¶

The frame is subscripted directly. Again, passing a singel value returns a series.

In [78]:
frame["primes"]
Out[78]:
a    11
b    13
c    17
d    19
e    23
Name: primes, dtype: int64

While a list returns a DataFrame

In [79]:
frame[["primes"]]
Out[79]:
primes
a 11
b 13
c 17
d 19
e 23
In [80]:
frame[["primes","0-4"]]
Out[80]:
primes 0-4
a 11 0
b 13 1
c 17 2
d 19 3
e 23 4

Instead of subscripting, the get-method can be used.

In [81]:
frame.get(["primes","0-4"])
Out[81]:
primes 0-4
a 11 0
b 13 1
c 17 2
d 19 3
e 23 4

For single columns, an attribute with the same name exists

In [82]:
frame.primes
Out[82]:
a    11
b    13
c    17
d    19
e    23
Name: primes, dtype: int64

But this fails, if the column-name is not a valid attribute-name

In [83]:
# Raises SyntaxError
#frame.0-4

For even more options have a look at the pandas-website: https://pandas.pydata.org/pandas-docs/stable/indexing.html