In [15]:
plt.figure(figsize = (16, 8))
seaborn.boxplot(data = wgi, orient = "h")
plt.show()
import pandas
import numpy
import matplotlib.pyplot as plt
import seaborn
seaborn.set_style("white")
from sklearn.decomposition import PCA
from sklearn.preprocessing import scale
wgi = pandas.read_csv("https://fxjollois.github.io/donnees/WGI/wgi2019.csv")
wgi.head(10)
| Country | Code | Voice and Accountability | Political Stability and Absence of Violence/Terrorism | Government Effectiveness | Regulatory Quality | Rule of Law | Control of Corruption | |
|---|---|---|---|---|---|---|---|---|
| 0 | Aruba | ABW | 1.294189 | 1.357372 | 1.029933 | 0.857360 | 1.263128 | 1.217238 |
| 1 | Andorra | ADO | 1.139154 | 1.615139 | 1.908749 | 1.228176 | 1.579939 | 1.234392 |
| 2 | Afghanistan | AFG | -0.988032 | -2.649407 | -1.463875 | -1.120555 | -1.713527 | -1.401076 |
| 3 | Angola | AGO | -0.777283 | -0.311101 | -1.117144 | -0.893871 | -1.054343 | -1.054683 |
| 4 | Anguilla | AIA | NaN | 1.367357 | 0.815824 | 0.846231 | 0.355737 | 1.234392 |
| 5 | Albania | ALB | 0.151805 | 0.118570 | -0.061331 | 0.274380 | -0.411179 | -0.528758 |
| 6 | Netherlands Antilles (former) | ANT | NaN | NaN | NaN | NaN | NaN | NaN |
| 7 | United Arab Emirates | ARE | -1.122036 | 0.703494 | 1.377221 | 0.979325 | 0.840219 | 1.106342 |
| 8 | Argentina | ARG | 0.600435 | -0.119978 | -0.086486 | -0.492753 | -0.430726 | -0.071071 |
| 9 | Armenia | ARM | 0.050043 | -0.506411 | -0.066817 | 0.249515 | -0.131276 | -0.184168 |
wgi.describe().round(2)
| Voice and Accountability | Political Stability and Absence of Violence/Terrorism | Government Effectiveness | Regulatory Quality | Rule of Law | Control of Corruption | |
|---|---|---|---|---|---|---|
| count | 204.00 | 211.00 | 209.00 | 209.00 | 209.00 | 209.00 |
| mean | 0.00 | 0.00 | -0.00 | 0.00 | 0.00 | 0.00 |
| std | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| min | -2.19 | -2.77 | -2.45 | -2.40 | -2.35 | -1.77 |
| 25% | -0.79 | -0.55 | -0.68 | -0.69 | -0.72 | -0.76 |
| 50% | 0.09 | 0.07 | -0.07 | -0.11 | -0.12 | -0.18 |
| 75% | 0.90 | 0.84 | 0.71 | 0.85 | 0.69 | 0.70 |
| max | 1.69 | 1.90 | 2.22 | 2.16 | 2.02 | 2.17 |
plt.figure(figsize = (16, 8))
seaborn.boxplot(data = wgi, orient = "h")
plt.show()
wgi.isna().sum()
Country 0 Code 0 Voice and Accountability 10 Political Stability and Absence of Violence/Terrorism 3 Government Effectiveness 5 Regulatory Quality 5 Rule of Law 5 Control of Corruption 5 dtype: int64
wgi_complet = wgi[~wgi.isna().any(axis = 1)].reset_index()
wgi_complet.head(10)
| index | Country | Code | Voice and Accountability | Political Stability and Absence of Violence/Terrorism | Government Effectiveness | Regulatory Quality | Rule of Law | Control of Corruption | |
|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | Aruba | ABW | 1.294189 | 1.357372 | 1.029933 | 0.857360 | 1.263128 | 1.217238 |
| 1 | 1 | Andorra | ADO | 1.139154 | 1.615139 | 1.908749 | 1.228176 | 1.579939 | 1.234392 |
| 2 | 2 | Afghanistan | AFG | -0.988032 | -2.649407 | -1.463875 | -1.120555 | -1.713527 | -1.401076 |
| 3 | 3 | Angola | AGO | -0.777283 | -0.311101 | -1.117144 | -0.893871 | -1.054343 | -1.054683 |
| 4 | 5 | Albania | ALB | 0.151805 | 0.118570 | -0.061331 | 0.274380 | -0.411179 | -0.528758 |
| 5 | 7 | United Arab Emirates | ARE | -1.122036 | 0.703494 | 1.377221 | 0.979325 | 0.840219 | 1.106342 |
| 6 | 8 | Argentina | ARG | 0.600435 | -0.119978 | -0.086486 | -0.492753 | -0.430726 | -0.071071 |
| 7 | 9 | Armenia | ARM | 0.050043 | -0.506411 | -0.066817 | 0.249515 | -0.131276 | -0.184168 |
| 8 | 11 | Antigua and Barbuda | ATG | 0.760444 | 0.959709 | -0.003870 | 0.485375 | 0.405205 | 0.277898 |
| 9 | 12 | Australia | AUS | 1.315125 | 1.086503 | 1.571896 | 1.873539 | 1.734145 | 1.811107 |
wgi_num = wgi_complet[wgi.columns[2:]]
wgi_num
| Voice and Accountability | Political Stability and Absence of Violence/Terrorism | Government Effectiveness | Regulatory Quality | Rule of Law | Control of Corruption | |
|---|---|---|---|---|---|---|
| 0 | 1.294189 | 1.357372 | 1.029933 | 0.857360 | 1.263128 | 1.217238 |
| 1 | 1.139154 | 1.615139 | 1.908749 | 1.228176 | 1.579939 | 1.234392 |
| 2 | -0.988032 | -2.649407 | -1.463875 | -1.120555 | -1.713527 | -1.401076 |
| 3 | -0.777283 | -0.311101 | -1.117144 | -0.893871 | -1.054343 | -1.054683 |
| 4 | 0.151805 | 0.118570 | -0.061331 | 0.274380 | -0.411179 | -0.528758 |
| ... | ... | ... | ... | ... | ... | ... |
| 197 | 0.026626 | -0.091665 | 0.019079 | 0.113867 | -0.119070 | -0.445551 |
| 198 | 0.670388 | -0.217931 | 0.367380 | 0.156172 | -0.076408 | 0.084924 |
| 199 | -1.365966 | -1.808007 | -1.627429 | -1.509667 | -1.786088 | -1.538931 |
| 200 | -0.286199 | -0.102216 | -0.675215 | -0.554269 | -0.462069 | -0.640345 |
| 201 | -1.141875 | -0.920179 | -1.205337 | -1.463199 | -1.257009 | -1.238796 |
202 rows × 6 columns
pca = PCA(n_components = 6)
pca.fit(wgi_num)
PCA(n_components=6)In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
PCA(n_components=6)
eig = pandas.DataFrame(
{
"Dimension" : ["Dim" + str(x + 1) for x in range(6)],
"Valeur propre" : pca.explained_variance_,
"% variance expliquée" : numpy.round(pca.explained_variance_ratio_ * 100),
"% cum. var. expliquée" : numpy.round(numpy.cumsum(pca.explained_variance_ratio_) * 100)
},
columns = ["Dimension", "Valeur propre", "% variance expliquée", "% cum. var. expliquée"]
)
eig
| Dimension | Valeur propre | % variance expliquée | % cum. var. expliquée | |
|---|---|---|---|---|
| 0 | Dim1 | 5.049592 | 84.0 | 84.0 |
| 1 | Dim2 | 0.414679 | 7.0 | 91.0 |
| 2 | Dim3 | 0.307597 | 5.0 | 96.0 |
| 3 | Dim4 | 0.121650 | 2.0 | 98.0 |
| 4 | Dim5 | 0.049650 | 1.0 | 99.0 |
| 5 | Dim6 | 0.040692 | 1.0 | 100.0 |
plt.figure(figsize=(16, 6))
g_eig = seaborn.barplot(x = "Dimension",
y = "% variance expliquée",
color = "lightseagreen",
data = eig)
g_eig.set(ylabel = "Variance expliquée (%)")
g_eig.figure.suptitle("Variance expliquée par dimension")
plt.show()
wgi_proj = pandas.DataFrame(pca.transform(wgi_num)).rename(columns = {i: "Dim"+str(i+1) for i in range(6)}) \
.assign(Pays = wgi_complet.Country)
wgi_proj
| Dim1 | Dim2 | Dim3 | Dim4 | Dim5 | Dim6 | Pays | |
|---|---|---|---|---|---|---|---|
| 0 | -2.921523 | 0.503627 | 0.056127 | 0.152636 | 0.031572 | 0.082826 | Aruba |
| 1 | -3.630601 | 0.075195 | 0.445399 | -0.165326 | -0.194070 | 0.416103 | Andorra |
| 2 | 3.704414 | -0.846353 | -1.093568 | 0.134714 | -0.123744 | -0.112983 | Afghanistan |
| 3 | 2.083839 | 0.446336 | 0.242998 | -0.215133 | 0.050528 | -0.154599 | Angola |
| 4 | 0.137824 | 0.175896 | -0.119501 | -0.649779 | -0.141887 | -0.141638 | Albania |
| ... | ... | ... | ... | ... | ... | ... | ... |
| 197 | 0.134034 | -0.035217 | -0.094282 | -0.400461 | 0.001850 | 0.095660 | Serbia |
| 198 | -0.469483 | -0.010186 | -0.579558 | -0.067936 | -0.351600 | 0.124790 | South Africa |
| 199 | 3.856331 | -0.236763 | -0.284979 | 0.079236 | -0.088370 | -0.093258 | Congo, Dem. Rep. |
| 200 | 1.060152 | 0.400094 | 0.080514 | -0.119279 | 0.132326 | 0.005206 | Zambia |
| 201 | 2.887938 | 0.178088 | 0.191012 | 0.096906 | -0.050628 | 0.131672 | Zimbabwe |
202 rows × 7 columns
coordvar = pca.components_.T * numpy.sqrt(pca.explained_variance_)
coordvar_df = pandas.DataFrame(coordvar, columns=['Dim'+str(i) for i in range(1, 7)], index=wgi_num.columns)
fig, axes = plt.subplots(figsize = (10, 10))
fig.suptitle("Cercle des corrélations")
axes.set_xlim(-1, 1)
axes.set_ylim(-1, 1)
axes.axvline(x = 0, color = 'lightgray', linestyle = '--', linewidth = 1)
axes.axhline(y = 0, color = 'lightgray', linestyle = '--', linewidth = 1)
for j in range(5):
axes.text(coordvar_df["Dim1"].iloc[j],
coordvar_df["Dim2"].iloc[j],
coordvar_df.index[j], size = 25)
axes.plot([0,coordvar_df["Dim1"].iloc[j]],
[0,coordvar_df["Dim2"].iloc[j]],
color = "gray", linestyle = 'dashed')
plt.gca().add_artist(plt.Circle((0,0),1,color='blue',fill=False))
plt.show()
g_pca = seaborn.lmplot(x = "Dim1", y = "Dim2", data = wgi_proj, fit_reg = False,
height = 10, aspect = 1.5)
g_pca.set(xlabel = "Dimension 1 (83%)", ylabel = "Dimension 2 (8%)")
g_pca.fig.suptitle("Premier plan factoriel")
plt.show()
g_pca = seaborn.lmplot(x = "Dim1", y = "Dim2", data = wgi_proj, fit_reg = False,
height = 10, aspect = 1.5)
g_pca.set(xlabel = "Dimension 1 (83%)", ylabel = "Dimension 2 (8 %)")
plt.xlim(-6, 6)
for i in range(wgi_proj.shape[0]):
if (abs(wgi_proj.iloc[i,0]) > 4):
plt.text(wgi_proj.iloc[i,0], wgi_proj.iloc[i,1], wgi_proj.iloc[i,6], ha = "left", fontsize = 20)
if (abs(wgi_proj.iloc[i,1]) > 1.5):
plt.text(wgi_proj.iloc[i,0], wgi_proj.iloc[i,1], wgi_proj.iloc[i,6], ha = "center", fontsize = 20)
plt.show()
