#import usual libraries
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import scipy as sp
import statsmodels.api as sm

#import library to change country names from abbreviations to the full name.
!pip install country_converter --upgrade

#import library for heat map
!pip install geopandas
import geopandas as gpd
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#union density dataset
union = pd.read_csv('https://raw.githubusercontent.com/JulieChandlerDS/ILO_union_density/main/data-SmplN.csv')
#world happiness report 2019 (chosen because the union dataset has the most entries for 2019)
happiness = pd.read_csv('https://raw.githubusercontent.com/JulieChandlerDS/world-happiness-report/main/2019.csv')
#only use 2019 data since that's the most we have
union = union.loc[union['time']==2019.0]

#Data Cleaning

#remove unneccesary columns from union index, we just need the obs value and the name of the country
union = union.drop(['time', 'area_time', 'Column 1','Column 1.1','Column 1.2'], axis = 1)
#do the same for happiness
GDP = happiness.drop(['Overall rank', 'GDP per capita', 'Social support', 'Healthy life expectancy', 'Freedom to make life choices', 'Generosity', 'Perceptions of corruption'], axis = 1)

We'll center the data. This is as simple as subtracting the mean of the score from the observation score.

x − x̄

#centering data
union_mean = union['obs_value'].mean()
#happiness centering
happiness_mean = happiness['Score'].mean()
#centering data
union['obs_value'] = union['obs_value'] - union['obs_value'].mean()
GDP['Score'] = GDP['Score'] - GDP['Score'].mean()

Next we'll scale the data by way of means normalization. This simply means we divide by the standard deviation.

$ x' = \frac{x-\bar{x}(x)}{max(x)-min(x)}$

#Scaling data for happiness 
GDP['Score'] = (GDP['Score']-GDP['Score'].mean())/GDP['Score'].std()
#Scaling data for unions 
union['obs_value'] = (union['obs_value']-union['obs_value'].mean())/union['obs_value'].std()
GDP
Country or region Score
0 Finland 2.121877
1 Denmark 1.970052
2 Norway 1.928727
3 Iceland 1.874824
4 Netherlands 1.869434
... ... ...
151 Rwanda -1.862420
152 Tanzania -1.954952
153 Afghanistan -1.980107
154 Central African Republic -2.087912
155 South Sudan -2.294538

156 rows × 2 columns

import country_converter as coco
GDP['Country or region'] = coco.convert(names=GDP['Country or region'], to='ISO3')
GDP
Country or region Score
0 FIN 2.121877
1 DNK 1.970052
2 NOR 1.928727
3 ISL 1.874824
4 NLD 1.869434
... ... ...
151 RWA -1.862420
152 TZA -1.954952
153 AFG -1.980107
154 CAF -2.087912
155 SSD -2.294538

156 rows × 2 columns

GDP.rename(columns = {'Country or region':'ref_area'}, inplace = True)
#combine datasets
df = GDP.merge(union, how='left')
df
ref_area Score obs_value
0 FIN 2.121877 2.089948
1 DNK 1.970052 2.544855
2 NOR 1.928727 1.623946
3 ISL 1.874824 3.898480
4 NLD 1.869434 -0.317729
... ... ... ...
151 RWA -1.862420 -0.844755
152 TZA -1.954952 NaN
153 AFG -1.980107 -0.240062
154 CAF -2.087912 NaN
155 SSD -2.294538 NaN

156 rows × 3 columns

df
ref_area Score obs_value
0 FIN 2.121877 2.089948
1 DNK 1.970052 2.544855
2 NOR 1.928727 1.623946
3 ISL 1.874824 3.898480
4 NLD 1.869434 -0.317729
... ... ... ...
151 RWA -1.862420 -0.844755
152 TZA -1.954952 NaN
153 AFG -1.980107 -0.240062
154 CAF -2.087912 NaN
155 SSD -2.294538 NaN

156 rows × 3 columns

df.rename(columns={'Score':'GDP'}, inplace=True)
df.rename(columns={'obs_value':'Union Density'}, inplace=True)
df.rename(columns={'ref_area':'Country'}, inplace=True)
df = df.dropna()
df
Country GDP Union Density
0 FIN 2.121877 2.089948
1 DNK 1.970052 2.544855
2 NOR 1.928727 1.623946
3 ISL 1.874824 3.898480
4 NLD 1.869434 -0.317729
6 SWE 1.739169 2.444997
9 AUT 1.652027 0.281417
11 CRI 1.581055 -0.034799
13 LUX 1.511880 0.392370
14 GBR 1.479539 0.126083
16 DEU 1.417551 -0.267800
17 BEL 1.361851 1.551827
26 GTM 0.924342 -1.000089
29 ESP 0.850676 -0.484158
30 PAN 0.821029 0.286964
31 BRA 0.802163 -0.450872
33 SGP 0.768025 0.059511
35 ITA 0.732988 0.630918
36 BHR 0.711427 -1.027827
37 SVK 0.710529 -0.556277
41 LTU 0.666508 -0.761540
42 COL 0.644947 -0.911326
51 THA 0.539837 -0.988993
52 LVA 0.478748 -0.584015
54 EST 0.436524 -0.839207
57 JPN 0.430236 -0.240062
60 BOL 0.334109 -0.506348
61 HUN 0.315244 -0.689421
62 PRY 0.301768 -0.789278
70 MDA 0.109515 -0.140204
76 DOM 0.016084 -0.755992
78 TUR -0.030631 -0.622849
82 MNG -0.109688 0.536608
83 MKD -0.119570 -0.245609
88 MAR -0.178863 -0.567373
91 IDN -0.193237 -0.450872
97 GHA -0.369319 -0.240062
101 BEN -0.470835 0.592085
105 ZAF -0.615474 0.442298
109 PSE -0.638832 0.009582
110 SEN -0.652307 -0.761540
111 SOM -0.663986 -0.517444
115 ARM -0.761909 -0.034799
118 GEO -0.797844 -0.179038
120 KEN -0.806828 -0.633944
123 TUN -0.849950 0.941586
129 LKA -0.935296 -0.611754
132 UKR -0.965840 0.858372
133 ETH -1.007166 -0.650587
137 ZMB -1.167975 0.153821
138 TGO -1.187739 0.148273
143 LSO -1.441980 -0.905779
151 RWA -1.862420 -0.844755
153 AFG -1.980107 -0.240062

#Visualization

###Scatter Plot

#scatter plot
plt.style.use('fivethirtyeight')
plt.scatter(df['GDP'], df['Union Density'])
plt.title("correlation between GDP and union density")
plt.xlabel("GDP")
plt.ylabel("union density")
plt.show();

###Histograms

plt.hist(df['GDP'])
plt.show()

plt.hist(df['Union Density'])
plt.show()

###Heat Map

import seaborn as sns
# Extract relevant columns from the dataframe
corr_df = df[['Union Density', 'GDP']]

# Compute the correlation matrix
corr_matrix = corr_df.corr()

# Plot the heatmap
sns.heatmap(corr_matrix, annot=True, cmap='coolwarm', linewidths=0.5)

# Add title and axis labels
plt.title('Correlation Heatmap of Union Density and GDP per capita')
plt.xlabel('Variable')
plt.ylabel('Variable')

# Show the plot
plt.show()

#Machine learning

###Pooled Linear regression

A linear regression seems most appropriate for our testing of one variable to cause another, since that's it's usual use.

Yi = f(Xi,β) + ei

y_var_name = 'GDP_PCAP_GWTH_PCNT'
X_var_names = ['GCF_GWTH_PCNT']
#linear regression
import seaborn as sns
plt.style.use('fivethirtyeight')
plt.title("correlation between happiness and union density")
plt.xlabel("happiness")
plt.ylabel("union density")
sns.regplot(data=df, y= df['Union Density'], x = df['GDP']);

#pooled linear regression
import seaborn as sns
plt.style.use('fivethirtyeight')
plt.title("correlation between GDP and union density")
plt.xlabel("GDP")
plt.ylabel("union density")
sns.regplot(data=df, y= df['Union Density'], x = df['GDP']);

#K-means clustering

from sklearn.cluster import KMeans

# Extract relevant columns from the dataframe
X = df[['Union Density', 'GDP']]

# Define number of clusters
k = 4

# Fit KMeans algorithm to the data
kmeans = KMeans(n_clusters=k, random_state=0).fit(X)

# Add a new column to the dataframe with the cluster labels
df['Cluster'] = kmeans.labels_

# Plot the clusters
plt.scatter(df['Union Density'], df['GDP'], c=df['Cluster'])
plt.xlabel('Union Density')
plt.ylabel('GDP per capita')
plt.title('K-means clustering of union density and GDP per capita')
plt.show()
/usr/local/lib/python3.9/dist-packages/sklearn/cluster/_kmeans.py:870: FutureWarning: The default value of `n_init` will change from 10 to 'auto' in 1.4. Set the value of `n_init` explicitly to suppress the warning
  warnings.warn(
<ipython-input-22-131ce7215dc0>:13: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  df['Cluster'] = kmeans.labels_

#Correlation or causation

OLS, or Ordinary least squares, gives us some estimates of values in our linear regression by minimizing the sum of squares in the line that was fit to our data.

β̂ = (X⊤X)−1X⊤y

#OLS for union density vs GDP
np.random.seed(9876789)

X = df['GDP']
y = df['Union Density']

model = sm.OLS(y, X, missing='drop')
results = model.fit()
results.summary()
OLS Regression Results
Dep. Variable: Union Density R-squared (uncentered): 0.190
Model: OLS Adj. R-squared (uncentered): 0.175
Method: Least Squares F-statistic: 12.42
Date: Sat, 08 Apr 2023 Prob (F-statistic): 0.000886
Time: 18:56:43 Log-Likelihood: -70.649
No. Observations: 54 AIC: 143.3
Df Residuals: 53 BIC: 145.3
Df Model: 1
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
GDP 0.4025 0.114 3.524 0.001 0.173 0.632
Omnibus: 15.667 Durbin-Watson: 1.581
Prob(Omnibus): 0.000 Jarque-Bera (JB): 18.327
Skew: 1.166 Prob(JB): 0.000105
Kurtosis: 4.646 Cond. No. 1.00


Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.

This OLS regression result suggests a statistically significant, positive relationship between union density and GDP.

The coefficient GDP variable being 0.4025 means that for every unit increase in GDP, the union density increases by an average of 0.4025 units. The p-value for the GDP variable is very small (0.001), indicating that the relationship between union density and GDP is statistically significant at the 0.05 level.

The R-squared value of 0.190 suggests about 19% of the variance in uGDP can be explained by variation in union density. This indicates a moderate association between the two variables.

It's important to note that correlation does not necessarily imply causation, and there may be other factors that are influencing both union density and GDP. Additionally, the OLS regression assumes a linear relationship between the variables, and there may be non-linear relationships or interactions that are not captured by this model. Further research would be needed to determine the causal relationship, if any, between union density and GDP.

##Pooled OLS

# Define X and y variables 

y_var_name = df['Union Density']
X_var_names = df['GDP']
# Carve out y variable
pooled_y= y_var_name
# Carve out X variable
pooled_X= X_var_names
# Add the placeholder for the regression intercept. When the model is fitted, the coefficient of this variable is the regression model’s intercept β_0.
pooled_X = sm.add_constant(pooled_X)
#Build the OLS regression model:

pooled_olsr_model = sm.OLS(endog=pooled_y, exog=pooled_X)
#Train the model on the (y, X) data set and fetch the training results:

pooled_olsr_model_results = pooled_olsr_model.fit()
#Print the training summary:
print(pooled_olsr_model_results.summary())
                            OLS Regression Results                            
==============================================================================
Dep. Variable:          Union Density   R-squared:                       0.197
Model:                            OLS   Adj. R-squared:                  0.182
Method:                 Least Squares   F-statistic:                     12.78
Date:                Sat, 08 Apr 2023   Prob (F-statistic):           0.000765
Time:                        18:56:44   Log-Likelihood:                -70.391
No. Observations:                  54   AIC:                             144.8
Df Residuals:                      52   BIC:                             148.8
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const         -0.0897      0.127     -0.707      0.483      -0.344       0.165
GDP            0.4216      0.118      3.575      0.001       0.185       0.658
==============================================================================
Omnibus:                       14.562   Durbin-Watson:                   1.596
Prob(Omnibus):                  0.001   Jarque-Bera (JB):               16.366
Skew:                           1.119   Prob(JB):                     0.000279
Kurtosis:                       4.506   Cond. No.                         1.28
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

###Pearson Correlation

The Pearson correlation coefficient finds a linear relationship between two datasets. Similar to other correlation coefficients, this one varies between -1 and +1 with 0 implying no correlation. Correlations of -1 or +1 imply an exact linear relationship.

Note that the p-value relies on a normal distribution.

$r = \frac{\Sigma(x-m_x)(y-m_y)}{\sqrt\Sigma(x-m_x)^2\Sigma(y-m_y)^2}$

np.isnan(X).any()
np.isnan(y).any()

np.isinf(X).any()
np.isinf(y).any()
False
X = np.nan_to_num(X)
y = np.nan_to_num(y)
sp.stats.pearsonr(X, y)
PearsonRResult(statistic=0.44422304265859053, pvalue=0.0007654853445457307)

To put it plainly, this means that countries with higher union density tend to have higher GDP per capita on average. However, correlation does not necessarily imply causation, and there may be other factors that are influencing both union density and GDP per capita. Further research would be needed to determine the causal relationship, if any, between union density and GDP per capita.

!jupyter nbconvert --to html "/content/Union_density_to_gdp_per_capita_correlation (3).ipynb"
[NbConvertApp] WARNING | pattern '/content/Union_density_to_gdp_per_capita_correlation (3).ipynb' matched no files
This application is used to convert notebook files (*.ipynb)
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        WARNING: THE COMMANDLINE INTERFACE MAY CHANGE IN FUTURE RELEASES.

Options
=======
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as listed in the "Equivalent to" description-line of the aliases.
To see all configurable class-options for some <cmd>, use:
    <cmd> --help-all

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                can only be used when converting one notebook at a time.
    Default: ''
    Equivalent to: [--NbConvertApp.output_base]
--output-dir=<Unicode>
    Directory to write output(s) to. Defaults
                                  to output to the directory of each notebook. To recover
                                  previous default behaviour (outputting to the current
                                  working directory) use . as the flag value.
    Default: ''
    Equivalent to: [--FilesWriter.build_directory]
--reveal-prefix=<Unicode>
    The URL prefix for reveal.js (version 3.x).
            This defaults to the reveal CDN, but can be any url pointing to a copy
            of reveal.js.
            For speaker notes to work, this must be a relative path to a local
            copy of reveal.js: e.g., "reveal.js".
            If a relative path is given, it must be a subdirectory of the
            current directory (from which the server is run).
            See the usage documentation
            (https://nbconvert.readthedocs.io/en/latest/usage.html#reveal-js-html-slideshow)
            for more details.
    Default: ''
    Equivalent to: [--SlidesExporter.reveal_url_prefix]
--nbformat=<Enum>
    The nbformat version to write.
            Use this to downgrade notebooks.
    Choices: any of [1, 2, 3, 4]
    Default: 4
    Equivalent to: [--NotebookExporter.nbformat_version]

Examples
--------

    The simplest way to use nbconvert is

            > jupyter nbconvert mynotebook.ipynb --to html

            Options include ['asciidoc', 'custom', 'html', 'latex', 'markdown', 'notebook', 'pdf', 'python', 'rst', 'script', 'slides', 'webpdf'].

            > jupyter nbconvert --to latex mynotebook.ipynb

            Both HTML and LaTeX support multiple output templates. LaTeX includes
            'base', 'article' and 'report'.  HTML includes 'basic', 'lab' and
            'classic'. You can specify the flavor of the format used.

            > jupyter nbconvert --to html --template lab mynotebook.ipynb

            You can also pipe the output to stdout, rather than a file

            > jupyter nbconvert mynotebook.ipynb --stdout

            PDF is generated via latex

            > jupyter nbconvert mynotebook.ipynb --to pdf

            You can get (and serve) a Reveal.js-powered slideshow

            > jupyter nbconvert myslides.ipynb --to slides --post serve

            Multiple notebooks can be given at the command line in a couple of
            different ways:

            > jupyter nbconvert notebook*.ipynb
            > jupyter nbconvert notebook1.ipynb notebook2.ipynb

            or you can specify the notebooks list in a config file, containing::

                c.NbConvertApp.notebooks = ["my_notebook.ipynb"]

            > jupyter nbconvert --config mycfg.py

To see all available configurables, use `--help-all`.