Submitted:
14 May 2025
Posted:
15 May 2025
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Abstract
Keywords:
1. Introduction
- How do the interactions between the quality of logistics performance and each of the ESG pillars vary by country?
- Does better logistics performance systematically have a positive impact on ESG results—and if so by which mechanisms?
2. Literature Review
3. Data and Methodology
4. Environmental Sustainability and Logistics Efficiency: A Multi-Method Analysis Using IV Regressions, Predictive Algorithms, and Clustering
4.1. Causal Estimation of Environmental Determinants of Logistics Performance Within the ESG Framework
- t=[2007;2023]
4.2. Environmental Determinants of Logistics Efficiency: Evidence from Machine Learning Analysis Under ESG Standards
4.3. Identifying Country Profiles: A Cluster Analysis of LPI and Environmental Indicators
5. Exploring the Interaction Between Social Factors and LPI in an ESG Context
5.1. Analyzing the S-Social Component’s Impact on Logistics Performance
- t=[2007;2023].
5.2. Machine Learning Estimation of Socio-Economic Impacts on Logistics Performance
5.3. Clustering to Verify the Relationship Between LPI and the S-Social Component of the ESG Model
6. Governance and Logistics Performance: An Empirical Assessment within the ESG Framework
6.1. The Role of Institutional Governance in Shaping Logistics Efficiency: An ESG Perspective
- t=[2007;2023].
6.2. Machine Learning Regressions LPI and G-Governance
6.3. Clustering Governance Profiles and Their Impact on Logistics Performance
7. Policy Implications
8. Conclusions
Abbreviations
| LPI | Logistic Performance Index |
| AAGRPCI | Annualized average growth rate in per capita real survey mean consumption or income, total population (%) |
| ACFTC | Access to clean fuels and technologies for cooking (% of population) |
| AFFVA | Agriculture, forestry, and fishing, value added (% of GDP) |
| AFWT | Annual freshwater withdrawals, total (% of internal resources) |
| ALPA | Agricultural land (% of land area) |
| ASFD | Adjusted savings: net forest depletion (% of GNI) |
| ASNRD | Adjusted savings: natural resources depletion (% of GNI) |
| CDD | Cooling Degree Days |
| CET | Children in employment, total (% of children ages 7–14) |
| CO2E | CO2 emissions (metric tons per capita) |
| CODCDMPN | Cause of death, by communicable diseases and maternal, prenatal and nutrition conditions (% of total) |
| EILPE | Energy intensity level of primary energy (MJ/$2017 PPP GDP) |
| ESRPS | Economic and Social Rights Performance Score |
| EU | Energy use (kg of oil equivalent per capita) |
| FFEC | Fossil fuel energy consumption (% of total) |
| FPI | Food production index (2014–2016 = 100) |
| FRT | Fertility rate, total (births per woman) |
| GDPG | GDP growth (annual %) |
| GEE | Government Effectiveness: Estimate |
| GEET | Government expenditure on education, total (% of government expenditure) |
| GHGLUCF | GHG net emissions/removals by LUCF (Mt of CO2 equivalent) |
| GI | Gini index |
| HB | Hospital beds (per 1,000 people) |
| HDD | Heating Degree Days |
| HI35 | Heat Index 35 |
| ISL20 | Income share held by lowest 20% |
| IUI | Individuals using the Internet (% of population) |
| LEBT | Life expectancy at birth, total (years) |
| LFPRT | Labor force participation rate, total (% of population ages 15–64) (modeled ILO estimate) |
| LRAT | Literacy rate, adult total (% of people ages 15 and above) |
| LST | Land Surface Temperature |
| LWS | Level of water stress: freshwater withdrawal as a proportion of available freshwater resources |
| MRU5 | Mortality rate, under-5 (per 1,000 live births) |
| MST | Mammal species, threatened |
| NM | Net migration |
| NOE | Nitrous oxide emissions (metric tons of CO2 equivalent per capita) |
| PD | Population density (people per sq. km of land area) |
| PHRNPL | Poverty headcount ratio at national poverty lines (% of population) |
| PM2.5AE | PM2.5 air pollution, mean annual exposure (µg/m³) |
| POA | Prevalence of overweight (% of adults) |
| PSAOV | Political Stability and Absence of Violence/Terrorism: Estimate |
| PSHWNP | Proportion of seats held by women in national parliaments (%) |
| PSMS | People using safely managed sanitation services (% of population) |
| PSMWS | People using safely managed drinking water services (% of population) |
| REC | Renewable energy consumption (% of total final energy consumption) |
| RFMLFPR | Ratio of female to male labor force participation rate (%) (modeled ILO estimate) |
| RLE | Rule of Law: Estimate |
| RQE | Regulatory Quality: Estimate |
| SEP | School enrollment, primary (% gross) |
| SLRI | Strength of legal rights index (0=weak to 12=strong) |
| SPEI | Standardised Precipitation-Evapotranspiration Index |
| STJA | Scientific and technical journal articles |
| TMPA | Terrestrial and marine protected areas (% of total territorial area) |
| VAE | Voice and Accountability: Estimate |
Appendix A. Hyper Parameters of Regression Algorithms
| Category | Option | Setting |
| Data Split Preferences | Holdout Test Data - Sample | 20% of all data |
| Training and Validation Data - Sample | 20% for validation data | |
| Training Parameters | Weights | Linear |
| Degree (for polynomial kernel) | 3 | |
| Gamma parameter | 1 | |
| r parameter | 0 | |
| Tolerance of termination criterion | 0.001 | |
| Epsilon | 0.01 | |
| Scale features | ✔️ Enabled | |
| Set seed | 1 | |
| Costs of Constraints Violation | Costs settings | Optimized |
| Max. violation cost | 5 |
| Data Split Preferences | Holdout Test Data - Sample | 20% of all data |
| Training and Validation Data - Sample | 20% for validation data | |
| Training Parameters | Penalty | Lasso |
| Include intercept | ✔️ Enabled | |
| Scale features | ✔️ Enabled | |
| Set seed | 1 | |
| Lambda (λ) Settings | Selection | Optimized |
| Fixed value (if selected) | 1 (not selected) | |
| Largest λ within 1 SE of min | ❌ Disabled |
| Split Preferences | Holdout Test Data - Sample | 20% of all data |
| Training and Validation Data - Sample | 20% for validation data | |
| Training Parameters | Training data used per tree | 50% |
| Features per split | Auto | |
| Scale features | ✔️ Enabled | |
| Set seed | 1 | |
| Number of Trees | Tree selection | Optimized |
| Maximum number of trees | 100 |
| Category | Option | Setting |
| Data Split Preferences | Holdout Test Data - Sample | 20% of all data |
| Add generated indicator to data | ❌ Disabled | |
| Test set indicator | None (not selected) | |
| Training Parameters | Include intercept | ✔️ Enabled |
| Scale features | ✔️ Enabled | |
| Set seed | 1 |
| Category | Option | Setting |
| Data Split Preferences | Holdout Test Data - Sample | 20% of all data |
| Add generated indicator to data | ❌ Disabled | |
| Test set indicator | None (not selected) | |
| Training and Validation Data | Validation Sample | 20% for validation data |
| K-fold | ❌ Disabled | |
| Leave-one-out | ❌ Disabled | |
| Training Parameters | Weights | Rectangular |
| Distance | Euclidean | |
| Scale features | ✔️ Enabled | |
| Set seed | 1 | |
| Number of Nearest Neighbors | Selection Method | Optimized |
| Max. nearest neighbors | 10 | |
| Fixed nearest neighbors | ❌ Disabled |
| Category | Option | Setting |
| Data Split Preferences | Holdout Test Data - Sample | 20% of all data |
| Add generated indicator to data | ❌ Disabled | |
| Test set indicator | None (not selected) | |
| Training and Validation Data | Validation Sample | 20% for validation data |
| K-fold | ❌ Disabled | |
| Leave-one-out | ❌ Disabled | |
| Training Parameters | Min. observations for split | 20 |
| Min. observations in terminal node | 7 | |
| Max. interaction depth | 30 | |
| Scale features | ✔️️ Enabled | |
| Set seed | 1 | |
| Tree Complexity | Penalty Type | Optimized |
| Max. complexity penalty | 1 | |
| Fixed complexity penalty | ❌ Disabled (value: 0.01 grayed out) |
| Category | Option | Setting |
| Data Split Preferences | Holdout Test Data - Sample | 20% of all data |
| Add generated indicator to data | ❌ Disabled | |
| Test set indicator | None (not selected) | |
| Training and Validation Data | Validation Sample | 20% for validation data |
| K-fold cross-validation | ❌ Disabled | |
| Training Parameters | Shrinkage | 0.1 |
| Interaction depth | 1 | |
| Minimum observations in node | 10 | |
| Training data used per tree | 50% | |
| Loss function | Gaussian | |
| Scale features | ✔️️ Enabled | |
| Set seed | 1 | |
| Number of Trees | Tree selection | Optimized |
| Maximum number of trees | 100 | |
| Fixed number of trees | ❌ Disabled (value: 100 grayed out) |
Appendix B. Hyper Parameters of Clustering Algorithms
| Parameter | Value | Description |
| Epsilon neighborhood size | 2 | Maximum distance to include points in a point’s neighborhood (ε) |
| Min. core points | 5 | Minimum number of points required to form a core point |
| Distance | Normal | Type of distance used (likely Euclidean) |
| Scale features | Enabled | Features are scaled (normalized or standardized) |
| Set seed | Disabled | No seed set for result reproducibility |
| Category | Parameter | Value | Description |
| Algorithmic Settings | Max. iterations | 25 | Maximum number of iterations allowed during optimization |
| Fuzziness parameter | 2 | Degree of fuzziness in fuzzy clustering (e.g., Fuzzy C-Means) | |
| Scale features | Enabled (✓) | Features are scaled (standardized or normalized) | |
| Set seed | Disabled (✗) | No random seed set for reproducibility | |
| Cluster Determination | Determination method | Optimized according to BIC | Number of clusters determined by Bayesian Information Criterion (BIC) |
| Max. clusters | 10 | Maximum number of clusters to consider in optimization | |
| Clusters (Fixed) | 3 (disabled) | Fixed cluster number is not used |
| Parameter | Value | Description |
| Epsilon neighborhood size | 2 | Maximum distance to include points in a point’s neighborhood (ε) |
| Min. core points | 5 | Minimum number of points required to form a core point |
| Distance | Normal | Type of distance used (likely Euclidean) |
| Scale features | Enabled | Features are scaled (normalized or standardized) |
| Set seed | Disabled | No seed set for result reproducibility |
| Parameter | Value | Description |
| Center type | Means | Type of cluster center used (centroids) |
| Algorithm | Hartigan-Wong | Algorithm variant used for clustering (K-Means method) |
| Distance | Euclidean | Distance metric used for clustering |
| Max. iterations | 25 | Maximum number of iterations allowed |
| Random sets | 25 | Number of random initializations for better clustering |
| Scale features | Enabled (✓) | Features are scaled (standardized or normalized) |
| Set seed | Disabled (✗) | No random seed set for reproducibility |
| Cluster determination | Optimized (BIC) | Number of clusters determined using Bayesian Information Criterion (BIC) |
| Max. clusters | 10 | Maximum number of clusters to evaluate |
| Fixed clusters | Disabled (3 shown) | Fixed number of clusters not selected |
| Parameter | Value | Description |
| Model | Auto | Automatically selects the best clustering model |
| Max. iterations | 25 | Maximum number of iterations for model fitting |
| Scale features | Enabled (✓) | Features are scaled (standardized or normalized) |
| Set seed | Disabled (✗) | No seed set for reproducibility |
| Cluster determination | Optimized (BIC) | Number of clusters selected based on Bayesian Information Criterion (BIC) |
| Max. clusters | 10 | Maximum number of clusters to evaluate |
| Fixed clusters | Disabled (3 shown) | Fixed number of clusters not used |
| Parameter | Value | Description |
| Model | Auto | Automatically selects the best clustering model |
| Max. iterations | 25 | Maximum number of iterations for model fitting |
| Scale features | Enabled (✓) | Features are scaled (standardized or normalized) |
| Set seed | Disabled (✗) | No seed set for reproducibility |
| Cluster determination | Optimized (BIC) | Number of clusters selected based on Bayesian Information Criterion (BIC) |
| Max. clusters | 10 | Maximum number of clusters to evaluate |
| Fixed clusters | Disabled (3 shown) | Fixed number of clusters not used |
Appendix C. E-Enviromental Summary Statistics
| LPI | NOE | PM2.5AE | HI35 | ALPA | AFFVA | |
| Valid | 2771 | 2771 | 2771 | 2771 | 2771 | 2771 |
| Missing | 0 | 0 | 0 | 0 | 0 | 0 |
| Mode | 100.000 | -21.265 | 5.179 | 67.170 | 100.000 | 83.890 |
| Median | 2.760 | -21.265 | 4.830 | 67.170 | 72.900 | 83.890 |
| Mean | 10.854 | -21.265 | 5.177 | 67.169 | 65.608 | 83.909 |
| Std. Error of Mean | 0.497 | 1.688 | 0.054 | 0.330 | 0.686 | 0.154 |
| 95% CI Mean Upper | 11.828 | -17.955 | 5.283 | 67.817 | 66.954 | 84.211 |
| 95% CI Mean Lower | 9.880 | -24.576 | 5.071 | 66.521 | 64.262 | 83.607 |
| Std. Deviation | 26.155 | 88.873 | 2.852 | 17.387 | 36.134 | 8.104 |
| 95% CI Std. Dev. Upper | 26.862 | 91.277 | 2.929 | 17.857 | 37.111 | 8.324 |
| 95% CI Std. Dev. Lower | 25.484 | 86.593 | 2.779 | 16.941 | 35.207 | 7.897 |
| Coefficient of variation | 2.410 | -4.179 | 0.551 | 0.259 | 0.551 | 0.097 |
| MAD | 0.380 | 0.000 | 1.250 | 0.000 | 27.100 | 0.000 |
| MAD robust | 0.563 | 0.000 | 1.853 | 0.000 | 40.178 | 0.000 |
| IQR | 0.940 | 26.786 | 2.210 | 0.000 | 64.900 | 0.000 |
| Variance | 684.069 | 7.898.371 | 8.133 | 302.294 | 1.305.643 | 65.683 |
| 95% CI Variance Upper | 721.575 | 8.331.421 | 8.579 | 318.868 | 1.377.229 | 69.284 |
| 95% CI Variance Lower | 649.425 | 7.498.366 | 7.721 | 286.985 | 1.239.520 | 62.356 |
| Skewness | 2.986 | -4.217 | 2.322 | -1.261 | -0.650 | -3.304 |
| Std. Error of Skewness | 0.047 | 0.047 | 0.047 | 0.047 | 0.047 | 0.047 |
| Kurtosis | 6.984 | 26.820 | 7.759 | 3.475 | -1.067 | 18.588 |
| Std. Error of Kurtosis | 0.093 | 0.093 | 0.093 | 0.093 | 0.093 | 0.093 |
| Shapiro-Wilk | 0.336 | 0.551 | 0.796 | 0.754 | 0.826 | 0.483 |
| P-value of Shapiro-Wilk | < .001 | < .001 | < .001 | < .001 | < .001 | < .001 |
| Range | 99.810 | 1.044.803 | 23.950 | 100.000 | 99.800 | 77.688 |
| Minimum | 0.190 | -944.893 | 1.110 | 0.000 | 0.200 | 22.312 |
| Maximum | 100.000 | 99.910 | 25.060 | 100.000 | 100.000 | 100.000 |
| 25th percentile | 2.460 | -21.265 | 3.380 | 67.170 | 35.100 | 83.890 |
| 50th percentile | 2.760 | -21.265 | 4.830 | 67.170 | 72.900 | 83.890 |
| 75th percentile | 3.400 | 5.521 | 5.590 | 67.170 | 100.000 | 83.890 |
| 25th percentile | 2.460 | -21.265 | 3.380 | 67.170 | 35.100 | 83.890 |
| 50th percentile | 2.760 | -21.265 | 4.830 | 67.170 | 72.900 | 83.890 |
| 75th percentile | 3.400 | 5.521 | 5.590 | 67.170 | 100.000 | 83.890 |
| Sum | 30.076.280 | -58.926.381 | 14.345.898 | 186.125.522 | 181.800.321 | 232.511.799 |
| NOE | PM2.5AE | HI35 | ALPA | AFFVA | LPI | |
| NOE | 7.898.371 | -26.637 | -119.086 | 5.641 | -36.715 | -23.566 |
| PM2.5AE | -26.637 | 8.133 | -7.922 | -22.657 | -2.142 | -3.410 |
| HI35 | -119.086 | -7.922 | 302.294 | 245.815 | 17.297 | 86.509 |
| ALPA | 5.641 | -22.657 | 245.815 | 1.305.643 | 88.102 | 209.274 |
| AFFVA | -36.715 | -2.142 | 17.297 | 88.102 | 65.683 | 11.491 |
| LPI | -23.566 | -3.410 | 86.509 | 209.274 | 11.491 | 684.069 |
| NOE | PM2.5AE | HI35 | ALPA | AFFVA | LPI | |
| NOE | 1.000 | -0.105 | -0.077 | 0.002 | -0.051 | -0.010 |
| PM2.5AE | -0.105 | 1.000 | -0.160 | -0.220 | -0.093 | -0.046 |
| HI35 | -0.077 | -0.160 | 1.000 | 0.391 | 0.123 | 0.190 |
| ALPA | 0.002 | -0.220 | 0.391 | 1.000 | 0.301 | 0.221 |
| AFFVA | -0.051 | -0.093 | 0.123 | 0.301 | 1.000 | 0.054 |
| LPI | -0.010 | -0.046 | 0.190 | 0.221 | 0.054 | 1.000 |






Appendix D. S-Social Summary Statistics
| LPI | PSMWS | PSMS | PA65A | SEP | CET | POA | ISL20 | |
| Valid | 2771 | 2771 | 2771 | 2771 | 2771 | 2771 | 2771 | 2771 |
| Missing | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Mode | 100.000 | 2.500 | 70.660 | 7.346 | -0.176 | -0.115 | 21.092 | -0.046 |
| Median | 2.760 | 8.700 | 75.890 | 5.759 | -0.175 | -0.256 | 20.800 | -0.089 |
| Mean | 10.854 | 10.523 | 70.649 | 7.346 | -0.176 | -0.115 | 21.081 | -0.046 |
| Std. Error of Mean | 0.497 | 0.188 | 0.368 | 0.102 | 0.018 | 0.019 | 0.218 | 0.019 |
| 95% CI Mean Upper | 11.828 | 10.892 | 71.370 | 7.547 | -0.141 | -0.079 | 21.508 | -0.010 |
| 95% CI Mean Lower | 9.880 | 10.154 | 69.928 | 7.146 | -0.212 | -0.152 | 20.654 | -0.083 |
| Std. Deviation | 26.155 | 9.899 | 19.355 | 5.380 | 0.950 | 0.983 | 11.467 | 0.978 |
| 95% CI Std. Dev. Upper | 26.862 | 10.167 | 19.879 | 5.526 | 0.976 | 1.009 | 11.777 | 1.005 |
| 95% CI Std. Dev. Lower | 25.484 | 9.645 | 18.859 | 5.242 | 0.925 | 0.958 | 11.173 | 0.953 |
| Coefficient of variation | 2.410 | 0.941 | 0.274 | 0.732 | -5.389 | -8.514 | 0.544 | -21.161 |
| MAD | 0.380 | 5.700 | 10.464 | 2.491 | 0.635 | 0.644 | 7.526 | 0.686 |
| MAD robust | 0.563 | 8.451 | 15.514 | 3.693 | 0.941 | 0.955 | 11.158 | 1.017 |
| IQR | 0.940 | 9.400 | 23.747 | 5.737 | 1.279 | 1.352 | 14.860 | 1.381 |
| Variance | 684.069 | 97.998 | 374.634 | 28.946 | 0.902 | 0.966 | 131.488 | 0.957 |
| 95% CI Variance Upper | 721.575 | 103.371 | 395.175 | 30.533 | 0.952 | 1.019 | 138.698 | 1.010 |
| 95% CI Variance Lower | 649.425 | 93.035 | 355.661 | 27.480 | 0.857 | 0.917 | 124.829 | 0.909 |
| Skewness | 2.986 | 2.056 | -1.021 | 1.417 | -0.582 | 0.424 | 0.612 | 0.153 |
| Std. Error of Skewness | 0.047 | 0.047 | 0.047 | 0.047 | 0.047 | 0.047 | 0.047 | 0.047 |
| Kurtosis | 6.984 | 5.374 | 0.578 | 1.875 | 0.053 | -0.490 | 0.238 | -0.539 |
| Std. Error of Kurtosis | 0.093 | 0.093 | 0.093 | 0.093 | 0.093 | 0.093 | 0.093 | 0.093 |
| Shapiro-Wilk | 0.336 | 0.768 | 0.919 | 0.873 | 0.970 | 0.966 | 0.971 | 0.985 |
| P-value of Shapiro-Wilk | < .001 | < .001 | < .001 | < .001 | < .001 | < .001 | < .001 | < .001 |
| Range | 99.810 | 68.400 | 99.177 | 28.880 | 4.933 | 4.716 | 63.750 | 4.800 |
| Minimum | 0.190 | 2.500 | 7.345 | 0.100 | -3.313 | -2.591 | 0.000 | -2.548 |
| Maximum | 100.000 | 70.900 | 106.522 | 28.980 | 1.620 | 2.125 | 63.750 | 2.252 |
| 25th percentile | 2.460 | 2.500 | 60.459 | 3.688 | -0.714 | -0.823 | 12.531 | -0.741 |
| 50th percentile | 2.760 | 8.700 | 75.890 | 5.759 | -0.175 | -0.256 | 20.800 | -0.089 |
| 75th percentile | 3.400 | 11.900 | 84.206 | 9.425 | 0.566 | 0.529 | 27.391 | 0.640 |
| 25th percentile | 2.460 | 2.500 | 60.459 | 3.688 | -0.714 | -0.823 | 12.531 | -0.741 |
| 50th percentile | 2.760 | 8.700 | 75.890 | 5.759 | -0.175 | -0.256 | 20.800 | -0.089 |
| 75th percentile | 3.400 | 11.900 | 84.206 | 9.425 | 0.566 | 0.529 | 27.391 | 0.640 |
| Sum | 30.076.280 | 29.159.833 | 195.768.244 | 20.356.604 | -488.409 | -319.845 | 58.416.354 | -128.115 |
| ᵃ The mode is computed assuming that variables are discreet. | ||||||||





| LPI | PSMWS | PSMS | PA65A | SEP | CET | POA | ISL20 | |
| LPI | 684.069 | -39.318 | -71.754 | 8.334 | -0.339 | 1.931 | -28.347 | 2.105 |
| PSMWS | -39.318 | 97.998 | 0.399 | 4.457 | -3.922 | -4.956 | -18.778 | -4.947 |
| PSMS | -71.754 | 0.399 | 374.634 | -24.405 | 7.209 | 4.557 | 49.932 | 4.168 |
| PA65A | 8.334 | 4.457 | -24.405 | 28.946 | -0.350 | -0.248 | 0.497 | -0.241 |
| SEP | -0.339 | -3.922 | 7.209 | -0.350 | 0.902 | 0.725 | 2.395 | 0.652 |
| CET | 1.931 | -4.956 | 4.557 | -0.248 | 0.725 | 0.966 | 2.941 | 0.899 |
| POA | -28.347 | -18.778 | 49.932 | 0.497 | 2.395 | 2.941 | 131.488 | 2.807 |
| ISL20 | 2.105 | -4.947 | 4.168 | -0.241 | 0.652 | 0.899 | 2.807 | 0.957 |
| LPI | PSMWS | PSMS | PA65A | SEP | CET | POA | ISL20 | |
| LPI | 1.000 | -0.152 | -0.142 | 0.059 | -0.014 | 0.075 | -0.095 | 0.082 |
| PSMWS | -0.152 | 1.000 | 0.002 | 0.084 | -0.417 | -0.509 | -0.165 | -0.511 |
| PSMS | -0.142 | 0.002 | 1.000 | -0.234 | 0.392 | 0.240 | 0.225 | 0.220 |
| PA65A | 0.059 | 0.084 | -0.234 | 1.000 | -0.069 | -0.047 | 0.008 | -0.046 |
| SEP | -0.014 | -0.417 | 0.392 | -0.069 | 1.000 | 0.776 | 0.220 | 0.702 |
| CET | 0.075 | -0.509 | 0.240 | -0.047 | 0.776 | 1.000 | 0.261 | 0.935 |
| POA | -0.095 | -0.165 | 0.225 | 0.008 | 0.220 | 0.261 | 1.000 | 0.250 |
| ISL20 | 0.082 | -0.511 | 0.220 | -0.046 | 0.702 | 0.935 | 0.250 | 1.000 |
Appendix E. G-Governance Summary Statistics
| LPI | GEE | RQE | ESRPS | VAE | STJA | PSAOV | RLE | |
| Valid | 2771 | 2771 | 2771 | 2771 | 2771 | 2771 | 2771 | 2771 |
| Missing | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Mode | 100.000 | 45.761 | 16.506.420 | 67.641 | -0.137 | 25.367 | 912.876 | 0.543 |
| Median | 2.760 | 45.761 | 8.307.000 | 67.641 | -0.137 | 26.437 | 912.876 | 0.422 |
| Mean | 10.854 | 45.766 | 16.506.423 | 67.641 | -0.137 | 25.367 | 918.963 | 0.543 |
| Std. Error of Mean | 0.497 | 0.562 | 1.410.965 | 0.469 | 0.018 | 0.171 | 3.626.689 | 0.011 |
| 95% CI Mean Upper | 11.828 | 46.868 | 19.273.072 | 68.562 | -0.101 | 25.702 | 8.030.249 | 0.564 |
| 95% CI Mean Lower | 9.880 | 44.665 | 13.739.773 | 66.721 | -0.174 | 25.032 | -6.192.324 | 0.521 |
| Std. Deviation | 26.155 | 29.572 | 74.273.596 | 24.706 | 0.970 | 8.989 | 190.909.935 | 0.578 |
| 95% CI Std. Dev. Upper | 26.862 | 30.372 | 76.282.556 | 25.374 | 0.997 | 9.232 | 196.073.687 | 0.594 |
| 95% CI Std. Dev. Lower | 25.484 | 28.814 | 72.368.406 | 24.072 | 0.945 | 8.758 | 186.012.907 | 0.563 |
| Coefficient of variation | 2.410 | 0.646 | 4.500 | 0.365 | -7.064 | 0.354 | 207.745 | 1.065 |
| MAD | 0.380 | 26.861 | 8.199.420 | 15.044 | 0.756 | 5.062 | 13.807.876 | 0.139 |
| MAD robust | 0.563 | 39.825 | 12.156.460 | 22.305 | 1.121 | 7.504 | 20.471.557 | 0.207 |
| IQR | 0.940 | 53.576 | 16.340.420 | 27.922 | 1.505 | 11.438 | 26.629.000 | 0.289 |
| Variance | 684.069 | 874.520 | 5.517×10+9 | 610.394 | 0.942 | 80.803 | 3.645×10+10 | 0.334 |
| 95% CI Variance Upper | 721.575 | 922.468 | 5.819×10+9 | 643.861 | 0.993 | 85.233 | 3.844×10+10 | 0.353 |
| 95% CI Variance Lower | 649.425 | 830.231 | 5.237×10+9 | 579.481 | 0.894 | 76.711 | 3.460×10+10 | 0.318 |
| Skewness | 2.986 | 0.077 | 13.755 | -0.715 | -0.015 | -0.688 | -2.333 | 3.636 |
| Std. Error of Skewness | 0.047 | 0.047 | 0.047 | 0.047 | 0.047 | 0.047 | 0.047 | 0.047 |
| Kurtosis | 6.984 | -1.196 | 221.461 | -0.002 | -0.881 | 0.577 | 45.528 | 16.473 |
| Std. Error of Kurtosis | 0.093 | 0.093 | 0.093 | 0.093 | 0.093 | 0.093 | 0.093 | 0.093 |
| Shapiro-Wilk | 0.336 | 0.944 | 0.141 | 0.894 | 0.977 | 0.957 | 0.478 | 0.609 |
| P-value of Shapiro-Wilk | < .001 | < .001 | < .001 | < .001 | < .001 | < .001 | < .001 | < .001 |
| Range | 99.810 | 99.783 | 1.427×10+6 | 94.525 | 4.034 | 49.571 | 3.740×10+6 | 4.964 |
| Minimum | 0.190 | 0.217 | 1.000 | 5.475 | -2.259 | -5.258 | -2.290×10+6 | 0.018 |
| Maximum | 100.000 | 100.000 | 1.427×10+6 | 100.000 | 1.775 | 44.313 | 1.449×10+6 | 4.982 |
| 25th percentile | 2.460 | 18.005 | 166.000 | 61.593 | -0.909 | 19.500 | -17.033.000 | 0.254 |
| 50th percentile | 2.760 | 45.761 | 8.307.000 | 67.641 | -0.137 | 26.437 | 912.876 | 0.422 |
| 75th percentile | 3.400 | 71.581 | 16.506.420 | 89.516 | 0.596 | 30.938 | 9.596.000 | 0.543 |
| 25th percentile | 2.460 | 18.005 | 166.000 | 61.593 | -0.909 | 19.500 | -17.033.000 | 0.254 |
| 50th percentile | 2.760 | 45.761 | 8.307.000 | 67.641 | -0.137 | 26.437 | 912.876 | 0.422 |
| 75th percentile | 3.400 | 71.581 | 16.506.420 | 89.516 | 0.596 | 30.938 | 9.596.000 | 0.543 |
| Sum | 30.076.280 | 126.817.792 | 4.574×10+7 | 187.434.549 | -380.677 | 70.291.471 | 2.546×10+6 | 1.504.306 |
| ᵃ The mode is computed assuming that variables are discreet. | ||||||||



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| Dependent variable | LPI | |||||
| Endogenous | NOE PM25AE HI35 ALPA AFFVA | |||||
| Instruments | ACFTC PSMWS PSMS LEBT FRT PA65A LRAT SEP GEET CET LFPRT CODCDMPN MRU5 HB POA ISL20 GI PHRNPL AAGRPCI IUI GDPG PSHWNP RFMLFPR SLRI STJA RLE NM | |||||
| Observation | using 2771 observations | |||||
| Times | 17 | |||||
| Countries | 163 | |||||
| Fixed-effects TSLS | G2SLS random effects | |||||
| Variable | Coefficient | Std. Error | z-Statistic | Coefficient | Std. Error | z-Statistic |
| const | 4.36011** | 1.80629 | 2.414 | 4.30356** | 1.81460 | 2.372 |
| NOE | 0.00380304*** | 0.00124891 | 3.045 | 0.00382670*** | 0.00125502 | 3.049 |
| PM25AE | -0.109926** | 0.0434881 | -2.528 | -0.109655** | 0.0436855 | -2.510 |
| HI35 | 0.00822227*** | 0.00270937 | 3.035 | 0.00822599*** | 0.00272194 | 3.022 |
| ALPA | -0.00580407** | 0.00242142 | -2.397 | -0.00570789** | 0.00243231 | -2.347 |
| AFFVA | 0.0830939*** | 0.0217233 | 3.825 | 0.0836790*** | 0.0218238 | 3.834 |
| Statistics | SSR = 1880.24 | SSR = 2790.55 | ||||
| sigma-hat = 0.849903 (df = 2603) | sigma-hat = 1.00461 (df = 2765) | |||||
| R-squared = corr(y, yhat)^2 = 0.000173 | R-squared = corr(y, yhat)^2 = 0.000175 | |||||
| Included units = 163 | Included units = 163 | |||||
| Time-series length: min = 17, max = 17 | Time-series length: min = 17, max = 17 | |||||
| Wald chi-square(5) = 33.8617 [0.0000] | Wald chi-square(5) = 34.0125 [0.0000] | |||||
| Null hypothesis: The groups have a common intercept | sigma-hat(within) = 0.84990329 | |||||
| Test statistic: F(162, 2603) = 14978.8 [0.0000] | sigma-hat(between) = 25.712297 | |||||
| Statistics | Boosting Regression | Decision Tree Regression | k-Nearest Neighbours Regression | Linear Regression | Random Forest Regression | Lasso | Support Vector Machine |
| MSE | 668.052 | 435.315 | 596.462 | 603.118 | 464.679 | 606.449 | 842.876 |
| MSE(scaled) | 1.333 | 1.03 | 0.955 | 1.472 | 0.922 | 1.452 | 1.556 |
| RMSE | 25.847 | 20.864 | 24.423 | 24.558 | 21.556 | 24.626 | 29.032 |
| MAE / MAD | 13.713 | 8.824 | 8.57 | 14.267 | 10.264 | 14.032 | 9.458 |
| MAPE | 229.26% | 182.74% | 150.97% | 284.71% | 181.05% | 287.14% | 24.52% |
| R² | 0.111 | 0.234 | 0.272 | 0.069 | 0.29 | 0.074 | 0.049 |
| Variables | Mean decrease in accuracy | Total increase in node purity | Mean dropout loss |
| NOE | 277.497 | 114.677.766 | 23.130 |
| PM2.5AE | 224.074 | 107.476.889 | 21.434 |
| ALPA | 294.265 | 98.796.892 | 23.223 |
| HI35 | 237.642 | 77.966.120 | 21.182 |
| AFFVA | 16.990 | 30.634.277 | 17.586 |
| Metric | Density Based | Fuzzy C-Means | Hierarchical | Model Based | Neighborhood | Random Forest |
| Maximum diameter | 0.508 | 0.778 | 0.000 | 0.763 | 0.243 | 0.763 |
| Minimum separation | 1.000 | 0.008 | 0.184 | 0.000 | 0.026 | 3.16×10⁻⁵ |
| Pearson’s γ | 0.482 | 0.261 | 1.000 | 0.000 | 0.682 | 0.029 |
| Dunn index | 1.000 | 0.009 | 0.247 | 0.001 | 0.035 | 0.000 |
| Entropy | 0.000 | 0.709 | 0.266 | 0.940 | 0.941 | 0.695 |
| Calinski-Harabasz index | 0.099 | 0.060 | 0.161 | 0.000 | 1.000 | 0.000 |
| R² | 0.000 | 0.280 | 0.547 | 0.241 | 1.000 | 0.207 |
| AIC | 1.000 | 0.615 | 0.000 | 0.455 | 0.000 | 0.509 |
| BIC | 1.000 | 0.594 | 0.000 | 0.432 | 0.000 | 0.493 |
| Silhouette | 0.476 | 0.128 | 0.537 | 0.063 | 0.414 | 0.000 |
| Cluster | Noisepoints | 1 | 2 | 3 |
| Size | 8 | 2517 | 8 | 238 |
| Explained proportion within-cluster heterogeneity | 0.000 | 0.940 | 2.795×10-4 | 0.060 |
| Within sum of squares | 0.000 | 12160.403 | 3.617 | 776.706 |
| Silhouette score | 0.000 | 0.382 | 0.791 | 0.523 |
| Note. The Between Sum of Squares of the 3 cluster model is 3099.35 | ||||
| Note. The Total Sum of Squares of the 3 cluster model is 16040.08 | ||||
| LPI | NOE | PM2.5AE | HI35 | ALPA | AFFVA | |
| Cluster 0 | -0.073 | -1.314 | -1.612 | -0.328 | -7.928 | -0.504 |
| Cluster 1 | -0.016 | -0.062 | -0.044 | -0.305 | 0.037 | 0.011 |
| Cluster 2 | -0.027 | 0.423 | -2.623 | -0.329 | -2.766 | 0.843 |
| Cluster 3 | 0.169 | 0.684 | 0.606 | 3.250 | -0.033 | -0.125 |
| Y | LPI | |||||
| Endogenous | PSMWS PSMS PA65A SEP CET POA ISL20 | |||||
| Instruments | IUI GDPG PSHWNP RFMLFPR SLRI STJA RLE NM CO2E NOE PM25AE GHGLUCF EILPE REC FFEC EU CDD HDD HI35 SPEI LST PD LWS ALPA FPI AFFVA MST AFWT TMPA ASFD ASNRD | |||||
| T | 17 | |||||
| N | 163 | |||||
| Observations | 2771 | |||||
| Fixed-effects TSLS | G2SLS random effects | |||||
| coefficient | std. error | z | coefficient | std. error | z | |
| Constant | 14.2037*** | 0.931617 | 15.25 | 14.2130*** | 0.929932 | 15.28 |
| PSMWS | -0.0127591* | 0.00696445 | -1.832 | -0.0129694* | 0.00695574 | -1.865 |
| PSMS | -0.0485794*** | 0.0138711 | -3.502 | -0.0486587*** | 0.0138471 | -3.514 |
| PA65A | -0.0468931** | 0.0223795 | -2.095 | -0.0468441** | 0.0223481 | -2.096 |
| SEP | -0.364282** | 0.181080 | -2.012 | -0.363990** | 0.180837 | -2.013 |
| CET | 1.69526*** | 0.400538 | 4.232 | 1.69409*** | 0.399966 | 4.236 |
| POA | 0.0293510*** | 0.00888111 | 3.305 | 0.0292621*** | 0.00887040 | 3.299 |
| ISL20 | -1.59629*** | 0.370631 | -4.307 | -1.59533*** | 0.370088 | -4.311 |
| Statistics and Tests | SSR = 1043.01 | SSR = 2755.43 | ||||
| sigma-hat = 0.633248 (df = 2601) | sigma-hat = 0.998629 (df = 2763) | |||||
| R-squared = corr(y, yhat)^2 = 0.002318 | R-squared = corr(y, yhat)^2 = 0.002340 | |||||
| Included units = 163 | Included units = 163 | |||||
| Time-series length: min = 17, max = 17 | Time-series length: min = 17, max = 17 | |||||
| Wald chi-square(7) = 71.9868 [0.0000] | Wald chi-square(7) = 72.3664 [0.0000] | |||||
| Null hypothesis: The groups have a common intercept | sigma-hat(within) = 0.63324843 | |||||
| Test statistic: F(162, 2601) = 27100.4 [0.0000] | sigma-hat(between) = 26.654767 | |||||
| Metric | Boosting | Decision Tree | K-Nearest Neighbors | Linear | Random Forest | Regularized Linear | SVM |
| MSE | 0.617 | 0.110 | 0.000 | 0.451 | 0.007 | 0.642 | 0.708 |
| MSE(scaled) | 0.568 | 0.091 | 0.000 | 0.822 | 0.056 | 0.777 | 1.000 |
| RMSE | 0.643 | 0.099 | 0.000 | 0.470 | 0.005 | 0.664 | 0.724 |
| MAE / MAD | 0.776 | 0.140 | 0.000 | 0.727 | 0.277 | 0.857 | 0.316 |
| MAPE | 0.763 | 0.172 | 0.000 | 1.000 | 0.290 | 0.955 | 0.000 |
| R² | 0.211 | 0.793 | 1.000 | 0.092 | 0.950 | 0.103 | 0.000 |
| Metric | Density Based | Fuzzy C-Means | Hierarchical | Model Based | Neighborhood-Based | Random Forest |
|---|---|---|---|---|---|---|
| Maximum diameter | 1.000 | 0.072 | 0.063 | 0.967 | 0.061 | 0.081 |
| Minimum separation | 1.000 | 0.029 | 0.216 | 0.000 | 0.056 | 0.033 |
| Pearson’s γ | 0.527 | 0.000 | 0.870 | 0.179 | 0.538 | 0.056 |
| Dunn index | 1.000 | 0.043 | 0.314 | 0.000 | 0.081 | 0.043 |
| Entropy | 0.000 | 0.752 | 0.340 | 1.000 | 0.899 | 0.693 |
| Calinski-Harabasz index | 1.000 | 0.001 | 0.002 | 0.002 | 0.004 | 0.001 |
| R² | 0.000 | 0.351 | 0.642 | 0.627 | 1.000 | 0.494 |
| AIC | 1.000 | 0.593 | 0.000 | 0.008 | 0.000 | 0.569 |
| BIC | 1.000 | 0.593 | 0.000 | 0.008 | 0.000 | 0.569 |
| Silhouette | 1.000 | 0.115 | 0.926 | 0.370 | 0.963 | 0.000 |
| Cluster | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Size | 564 | 244 | 218 | 434 | 68 | 409 | 76 | 352 | 237 | 169 |
| Explained proportion within-cluster heterogeneity | 0.168 | 0.105 | 0.108 | 0.153 | 0.041 | 0.108 | 0.064 | 0.063 | 0.117 | 0.072 |
| Within sum of squares | 1.153 | 718.762 | 745.245 | 1.053 | 284.004 | 744.270 | 442.164 | 433.747 | 801.223 | 493.387 |
| Silhouette score | 0.227 | 0.161 | 0.219 | 0.194 | 0.378 | 0.239 | 0.235 | 0.450 | 0.204 | 0.430 |
| Center LPI | -0.302 | -0.315 | -0.324 | -0.312 | 3.309 | -0.299 | -0.327 | -0.277 | -0.311 | 3.233 |
| Center PSMWS | -0.077 | 0.164 | 2.259 | -0.088 | -0.042 | -0.515 | 1.799 | -0.673 | -0.127 | -0.632 |
| Center PSMS | 0.668 | 0.183 | 0.741 | -1.210 | -2.134 | -0.063 | -2.193 | 0.633 | 0.090 | 0.207 |
| Center PA65A | -0.624 | -0.466 | -0.165 | -0.078 | 1.284 | -0.121 | 1.423 | -0.220 | 2.149 | -0.252 |
| Center SEP | -0.253 | -0.209 | -0.691 | -0.662 | -1.185 | 0.883 | -2.489 | 1.200 | 0.242 | 0.358 |
| Center CET | -0.495 | -0.520 | -1.018 | -0.478 | -0.783 | 0.723 | -1.620 | 1.748 | 0.028 | 0.556 |
| Center POA | -0.360 | 1.542 | -0.600 | -0.400 | -0.580 | -0.505 | -0.423 | 1.168 | 0.147 | -0.217 |
| Center ISL20 | -0.545 | -0.474 | -1.035 | -0.416 | -0.978 | 0.751 | -1.560 | 1.603 | 0.114 | 0.685 |
| Cluster Means | ||||||||
| LPI | PSMWS | PSMS | PA65A | SEP | CET | POA | ISL20 | |
| Cluster 1 | -0.495 | -0.545 | -0.302 | -0.624 | -0.360 | 0.668 | -0.077 | -0.253 |
| Cluster 2 | -0.520 | -0.474 | -0.315 | -0.466 | 1.542 | 0.183 | 0.164 | -0.209 |
| Cluster 3 | -1.018 | -1.035 | -0.324 | -0.165 | -0.600 | 0.741 | 2.259 | -0.691 |
| Cluster 4 | -0.478 | -0.416 | -0.312 | -0.078 | -0.400 | -1.210 | -0.088 | -0.662 |
| Cluster 5 | -0.783 | -0.978 | 3.309 | 1.284 | -0.580 | -2.134 | -0.042 | -1.185 |
| Cluster 6 | 0.723 | 0.751 | -0.299 | -0.121 | -0.505 | -0.063 | -0.515 | 0.883 |
| Cluster 7 | -1.620 | -1.560 | -0.327 | 1.423 | -0.423 | -2.193 | 1.799 | -2.489 |
| Cluster 8 | 1.748 | 1.603 | -0.277 | -0.220 | 1.168 | 0.633 | -0.673 | 1.200 |
| Cluster 9 | 0.028 | 0.114 | -0.311 | 2.149 | 0.147 | 0.090 | -0.127 | 0.242 |
| Cluster 10 | 0.556 | 0.685 | 3.233 | -0.252 | -0.217 | 0.207 | -0.632 | 0.358 |
| y | LPI | |||||
| Endogenous | GEE RQE ESRPS VAE STJA PSAOV RLE | |||||
| Instruments | IUI CO2E NOE PM25AE GHGLUCF EILPE REC FFEC EU CDD HDD HI35 SPEI LSTPD LWS ALPA FPI AFFVA MST AFWT TMPA ASFD ASNRD | |||||
| T | 17 | |||||
| N | 163 | |||||
| Observations | 2771 | |||||
| G2SLS random effects | Fixed-effects TSLS | |||||
| coefficient | std. error | z | coefficient | std. error | z | |
| const | 11.9114*** | 0.588432 | 20.24 | 11.9297*** | 0.593942 | 20.09 |
| GEE | 0.0151558*** | 0.00230164 | 6.585 | 0.0152008*** | 0.00232277 | 6.544 |
| RQE | -5.51554e-06** | 2.38212e-06 | -2.315 | -5.52359e-06** | 2.40369e-06 | -2.298 |
| ESRPS | -0.0354579*** | 0.00975704 | -3.634 | -0.0357672 *** | 0.00984858 | -3.632 |
| VAE | 0.543244*** | 0.137306 | 3.956 | 0.546940 *** | 0.138589 | 3.946 |
| STJA | 0.0259654*** | 0.00625200 | 4.153 | 0.0259979*** | 0.00630913 | 4.121 |
| PSAOV | 9.78199e-07** | 4.06429e-07 | 2.407 | 9.77849e-07** | 4.10115e-07 | 2.384 |
| RLE | 0.282701** | 0.110445 | 2.560 | 0.283452** | 0.111451 | 2.543 |
| Statistics And Tests | SSR = 2713.7 | SSR = 1072.64 | ||||
| sigma-hat = 0.991039 (df = 2763) | sigma-hat = 0.64218 (df = 2601) | |||||
| R-squared = corr(y, yhat)^2 = 0.009367 | R-squared = corr(y, yhat)^2 = 0.009321 | |||||
| Included units = 163 | Included units = 163 | |||||
| Time-series length: min = 17, max = 17 | Time-series length: min = 17, max = 17 | |||||
| Wald chi-square(7) = 72.3551 [0.0000] | Wald chi-square(7) = 71.0526 [0.0000] | |||||
| sigma-hat(within) = 0.64218019 | Null hypothesis: The groups have a common intercept | |||||
| sigma-hat(between) = 30.771231 | Test statistic: F(162, 2601) = 26449.2 [0.0000] | |||||
| Boosting Regression | Decision Tree Regression | k-Nearest Neighbors | Linear Regressions | Random Forest Regression | Support Vector Machine | |
| MSE | 710.124 | 395.86 | 215.583 | 646.107 | 327.09 | 681.308 |
| MSE (scaled) | 1.198 | 0.759 | 0.425 | 1.488 | 0.415 | 1.689 |
| RMSE | 26.648 | 19.896 | 14.683 | 25.419 | 18.086 | 26.102 |
| MAE / MAD | 13.847 | 6.537 | 5.779 | 14.92 | 8.665 | 7.702 |
| MAPE | 212.44% | 128.57% | 133.26% | 294.11% | 145.91% | 18.16% |
| R² | 0.16 | 0.384 | 0.619 | 0.065 | 0.628 | 0.024 |
| Mean dropout loss | |
| STJA | 29.515 |
| VAE | 28.538 |
| ESRPS | 23.916 |
| RLE | 20.574 |
| GEE | 20.056 |
| RQE | 17.422 |
| PSAOV | 16.924 |
| Note. Mean dropout loss (defined as root mean squared error (RMSE)) is based on 50 permutations. | |
| Additive Explanations for Predictions of Test Set Cases | |||||||||
| Case | Predicted | Base | GEE | RQE | ESRPS | VAE | STJA | PSAOV | RLE |
| 1 | 2.180 | 10.678 | -0.686 | -0.046 | -16.907 | 9.827 | -0.116 | -0.529 | -0.042 |
| 2 | 2.370 | 10.678 | 0.019 | -0.002 | -16.008 | 9.862 | -1.659 | -0.550 | 0.029 |
| 3 | 6.203 | 10.678 | 0.493 | -0.006 | -14.116 | 7.964 | 0.773 | 0.172 | 0.245 |
| 4 | 2.370 | 10.678 | -0.387 | -0.015 | -16.067 | 9.473 | -0.832 | -0.417 | -0.062 |
| 5 | 2.503 | 10.678 | 2.120 | -1.209 | -0.858 | -1.044 | -5.932 | -0.239 | -1.014 |
| Note. Displayed values represent feature contributions to the predicted value without features (column ‘Base’) for the test set. | |||||||||
| Metric | Density Based | Fuzzy c-Means | Hierarchical | Model Based | Neighborhood | Random Forest |
| Maximum diameter | 0.447 | 0.740 | 0.000 | 0.791 | 0.057 | 1.000 |
| Minimum separation | 0.997 | 0.126 | 0.981 | 0.061 | 0.149 | 0.000 |
| Pearson’s γ | 0.805 | 0.368 | 1.000 | 0.283 | 0.588 | 0.000 |
| Dunn index | 0.492 | 0.046 | 1.000 | 0.000 | 0.110 | 0.001 |
| Entropy | 0.000 | 0.674 | 0.095 | 0.764 | 0.668 | 0.490 |
| Calinski-Harabasz index | 0.179 | 0.248 | 0.221 | 0.159 | 1.000 | 0.000 |
| R² | 0.130 | 0.425 | 0.392 | 0.297 | 1.000 | 0.000 |
| AIC | 0.699 | 0.273 | 0.327 | 0.578 | 0.000 | 1.000 |
| BIC | 0.672 | 0.258 | 0.333 | 0.578 | 0.000 | 1.000 |
| Silhouette | 0.787 | 0.328 | 0.704 | 0.463 | 0.598 | 0.000 |
| Cluster | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Size | 27 | 347 | 236 | 375 | 20 | 9 | 85 | 491 | 385 | 796 |
| Explained proportion within-cluster heterogeneity | 0.036 | 0.096 | 0.202 | 0.128 | 0.019 | 0.016 | 0.074 | 0.140 | 0.102 | 0.189 |
| Within sum of squares | 235.437 | 631.869 | 1.332.939 | 848.618 | 128.765 | 102.540 | 488.693 | 922.706 | 675.294 | 1.247.106 |
| Silhouette score | 0.391 | 0.342 | 0.263 | 0.149 | 0.458 | 0.684 | 0.315 | 0.155 | 0.317 | 0.243 |
| Center LPI | -0.052 | -0.282 | 3.251 | -0.311 | -0.276 | -0.277 | -0.307 | -0.302 | -0.314 | -0.312 |
| Center GEE | -0.851 | 1.256 | 0.415 | -0.128 | 0.923 | 0.398 | 0.011 | 0.711 | -1.064 | -0.534 |
| Center RQE | -0.144 | -0.127 | 0.237 | -0.107 | 2.339 | 15.237 | -0.125 | -0.164 | -0.051 | -0.051 |
| Center ESRPS | -0.480 | 1.169 | 0.657 | 0.159 | 0.830 | -0.000 | -0.178 | 0.543 | -1.892 | -0.185 |
| Center VAE | -0.744 | 1.378 | 0.075 | -1.335 | 0.794 | -1.503 | 0.705 | 0.520 | -0.639 | -0.059 |
| Center STJA | 0.732 | -1.684 | -0.117 | 0.986 | -0.415 | -0.697 | -0.154 | -0.205 | 0.482 | 0.207 |
| Center PSAOV | -6.510 | 0.371 | 0.273 | 0.012 | 5.663 | -0.853 | 0.190 | 0.045 | -0.170 | -0.126 |
| Center RLE | -0.512 | 0.190 | -0.117 | -0.271 | 0.198 | -0.236 | 4.396 | -0.044 | -0.246 | -0.229 |
| Note. The Between Sum of Squares of the 10 cluster model is 15546.03 | ||||||||||
| Note. The Total Sum of Squares of the 10 cluster model is 22160 | ||||||||||
| Cluster Means | ||||||||
| LPI | GEE | RQE | ESRPS | VAE | STJA | PSAOV | RLE | |
| Cluster 1 | -0.480 | -0.851 | -0.052 | -6.510 | -0.512 | -0.144 | 0.732 | -0.744 |
| Cluster 2 | 1.169 | 1.256 | -0.282 | 0.371 | 0.190 | -0.127 | -1.684 | 1.378 |
| Cluster 3 | 0.657 | 0.415 | 3.251 | 0.273 | -0.117 | 0.237 | -0.117 | 0.075 |
| Cluster 4 | 0.159 | -0.128 | -0.311 | 0.012 | -0.271 | -0.107 | 0.986 | -1.335 |
| Cluster 5 | 0.830 | 0.923 | -0.276 | 5.663 | 0.198 | 2.339 | -0.415 | 0.794 |
| Cluster 6 | -1.098×10-7 | 0.398 | -0.277 | -0.853 | -0.236 | 15.237 | -0.697 | -1.503 |
| Cluster 7 | -0.178 | 0.011 | -0.307 | 0.190 | 4.396 | -0.125 | -0.154 | 0.705 |
| Cluster 8 | 0.543 | 0.711 | -0.302 | 0.045 | -0.044 | -0.164 | -0.205 | 0.520 |
| Cluster 9 | -1.892 | -1.064 | -0.314 | -0.170 | -0.246 | -0.051 | 0.482 | -0.639 |
| Cluster 10 | -0.185 | -0.534 | -0.312 | -0.126 | -0.229 | -0.051 | 0.207 | -0.059 |
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