Supplementary Materials 3. Dependent variable: COVID-19 new cases per 100.000 inhabitants (14 day notification days) 28.10.2020 11.11.2020 25.11.2020 09.12.2020 23.12.2020 13.01.2021 27.01.2021 10.02.2021 24.02.2021 10.03.2021 24.03.2021 28.10.2020- 24.03.2021 median Predictors ulkoka19 Number of foreign citizens in residential building summed to postal code ko_perus Basic level studies, 2018 – no qualification after basic level or qualification unknown hr_mtu Median income of inhabitants, 2017 hr_pi_tul Inhabitants belonging to the lowest income category, 2017 tr_pi_tul Households belonging to the lowest income category, 2017 pt_tyott Unemployed, 2017 - people aged 15-64 years who were unemployed) pt_elakel Pensioners, 2017 ################################################################################ Global regression (OLS), Geographically Weighted Regression (GWR) and Multiscale Geographically Weighted Regression (MGWR) Results ################################################################################ 28.10.2020- 24.03.2021 median ================================================================================ Model type: Gaussian Number of observations: 69 Number of covariates: 4 Dependent variable: median Variable standardization: On Total runtime: 0:00:01 Global Regression Results -------------------------------------------------------------------------------- Residual sum of squares: 39.525 Log-likelihood: -78.684 AIC: 165.369 AICc: 168.321 R2: 0.427 Adj. R2: 0.401 Variable Est. SE t(Est/SE) p-value ------------------------------------ ---------- ---------- ---------- ---------- Intercept 0.000 0.094 0.000 1.000 ulkoka19 0.671 0.186 3.610 0.000 hr_mtu -0.345 0.110 -3.131 0.002 pt_elake -0.420 0.170 -2.476 0.013 ================================================================================ Geographically Weighted Regression (GWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AICc Bandwidth used: 67.000 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 33.439 Effective number of parameters (trace(S)): 7.703 Degree of freedom (n - trace(S)): 61.297 Sigma estimate: 0.739 Log-likelihood: -72.916 Degree of Dependency (DoD): 0.845 AIC: 163.238 AICc: 166.087 BIC: 182.682 R2: 0.515 Adj. R2: 0.453 Adj. alpha (95%): 0.026 Adj. critical t value (95%): 2.277 Summary Statistics For GWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept -0.000 0.070 -0.086 -0.021 0.147 ulkoka19 0.770 0.195 0.388 0.879 0.961 hr_mtu -0.266 0.134 -0.532 -0.207 -0.118 pt_elakel -0.456 0.130 -0.623 -0.505 -0.195 ================================================================================ Multiscale Geographically Weighted Regression (MGWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AICc Score of change (SOC) type: Smoothing f Termination criterion for MGWR: 1.0e-05 Number of iterations used: 23 MGWR bandwidths -------------------------------------------------------------------------------- Variable Bandwidth ENP_j Adj t-val(95%) DoD_j Intercept 67.000 1.956 2.283 0.841 ulkoka19 67.000 1.662 2.215 0.880 hr_mtu 63.000 2.350 2.358 0.798 pt_elakel 67.000 1.774 2.243 0.865 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 34.508 Effective number of parameters (trace(S)): 7.743 Degree of freedom (n - trace(S)): 61.257 Sigma estimate: 0.751 Log-likelihood: -74.002 Degree of Dependency (DoD): 0.844 AIC: 165.488 AICc: 168.363 BIC: 185.020 R2: 0.500 Adj. R2: 0.436 Summary Statistics For MGWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept -0.014 0.076 -0.099 -0.047 0.135 ulkoka19 0.613 0.070 0.511 0.643 0.700 hr_mtu -0.297 0.123 -0.537 -0.250 -0.151 pt_elakel -0.370 0.038 -0.433 -0.372 -0.316 ================================================================================ ################################################################################ 28.10.2020 ================================================================================ Model type: Gaussian Number of observations: 69 Number of covariates: 4 Dependent variable: case1028 Variable standardization: On Total runtime: 0:00:00 Global Regression Results -------------------------------------------------------------------------------- Residual sum of squares: 55.268 Log-likelihood: -90.251 AIC: 188.502 AICc: 191.454 R2: 0.199 Adj. R2: 0.162 Variable Est. SE t(Est/SE) p-value ------------------------------------ ---------- ---------- ---------- ---------- Intercept -0.000 0.111 -0.000 1.000 hr_mtu 0.386 0.130 2.965 0.003 pt_elakel -0.632 0.201 -3.148 0.002 ulkoka19 0.823 0.220 3.742 0.000 Geographically Weighted Regression (GWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AIC Bandwidth used: 66.000 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 48.107 Effective number of parameters (trace(S)): 7.911 Degree of freedom (n - trace(S)): 61.089 Sigma estimate: 0.887 Log-likelihood: -85.463 Degree of Dependency (DoD): 0.839 AIC: 188.749 AICc: 191.738 BIC: 208.657 R2: 0.303 Adj. R2: 0.211 Adj. alpha (95%): 0.025 Adj. critical t value (95%): 2.288 Summary Statistics For GWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept -0.003 0.109 -0.196 0.005 0.188 hr_mtu 0.360 0.112 0.145 0.381 0.489 pt_elakel -0.594 0.157 -0.854 -0.619 -0.284 ulkoka19 0.813 0.165 0.510 0.780 1.123 ================================================================================ Multiscale Geographically Weighted Regression (MGWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AIC Score of change (SOC) type: Smoothing f Termination criterion for MGWR: 1.0e-05 Number of iterations used: 34 MGWR bandwidths -------------------------------------------------------------------------------- Variable Bandwidth ENP_j Adj t-val(95%) DoD_j Intercept 55.000 2.772 2.423 0.759 hr_mtu 67.000 1.993 2.291 0.837 pt_elakel 51.000 2.816 2.430 0.755 ulkoka19 67.000 1.577 2.193 0.892 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 45.520 Effective number of parameters (trace(S)): 9.158 Degree of freedom (n - trace(S)): 59.842 Sigma estimate: 0.872 Log-likelihood: -83.556 Degree of Dependency (DoD): 0.804 AIC: 187.429 AICc: 191.348 BIC: 210.122 R2: 0.340 Adj. R2: 0.238 Summary Statistics For MGWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept -0.042 0.147 -0.272 -0.056 0.208 hr_mtu 0.281 0.066 0.166 0.319 0.353 pt_elakel -0.503 0.155 -0.813 -0.486 -0.238 ulkoka19 0.679 0.034 0.629 0.688 0.733 ================================================================================ ################################################################################ 11.11.2020 ================================================================================ Model type: Gaussian Number of observations: 69 Number of covariates: 3 Dependent variable: case1111 Variable standardization: On Total runtime: 0:00:00 Global Regression Results -------------------------------------------------------------------------------- Residual sum of squares: 56.085 Log-likelihood: -90.757 AIC: 187.514 AICc: 190.139 R2: 0.187 Adj. R2: 0.163 Variable Est. SE t(Est/SE) p-value ------------------------------------ ---------- ---------- ---------- ---------- Intercept 0.000 0.111 0.000 1.000 hr_pi_tul -0.441 0.237 -1.859 0.063 ko_perus 0.770 0.237 3.246 0.001 Geographically Weighted Regression (GWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AIC Bandwidth used: 68.000 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 52.447 Effective number of parameters (trace(S)): 4.966 Degree of freedom (n - trace(S)): 64.034 Sigma estimate: 0.905 Log-likelihood: -88.444 Degree of Dependency (DoD): 0.881 AIC: 188.819 AICc: 190.159 BIC: 202.148 R2: 0.240 Adj. R2: 0.180 Adj. alpha (95%): 0.030 Adj. critical t value (95%): 2.214 Summary Statistics For GWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept -0.011 0.082 -0.101 -0.054 0.163 hr_pi_tul -0.416 0.043 -0.484 -0.394 -0.355 ko_perus 0.772 0.059 0.672 0.756 0.882 ================================================================================ Multiscale Geographically Weighted Regression (MGWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AIC Score of change (SOC) type: Smoothing f Termination criterion for MGWR: 1.0e-05 Number of iterations used: 42 MGWR bandwidths -------------------------------------------------------------------------------- Variable Bandwidth ENP_j Adj t-val(95%) DoD_j Intercept 67.000 1.895 2.270 0.849 hr_pi_tul 67.000 1.728 2.232 0.871 ko_perus 67.000 1.655 2.214 0.881 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 51.482 Effective number of parameters (trace(S)): 5.277 Degree of freedom (n - trace(S)): 63.723 Sigma estimate: 0.899 Log-likelihood: -87.802 Degree of Dependency (DoD): 0.867 AIC: 188.159 AICc: 189.639 BIC: 202.182 R2: 0.254 Adj. R2: 0.191 Summary Statistics For MGWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept 0.011 0.101 -0.098 -0.036 0.200 hr_pi_tul -0.356 0.062 -0.448 -0.352 -0.245 ko_perus 0.725 0.075 0.626 0.726 0.853 ================================================================================ ################################################################################ 25.11.2020 ================================================================================ Model type: Gaussian Number of observations: 69 Number of covariates: 2 Dependent variable: case1125 Variable standardization: On Total runtime: 0:00:00 Global Regression Results -------------------------------------------------------------------------------- Residual sum of squares: 62.632 Log-likelihood: -94.566 AIC: 193.132 AICc: 195.501 R2: 0.092 Adj. R2: 0.079 Variable Est. SE t(Est/SE) p-value ------------------------------------ ---------- ---------- ---------- ---------- Intercept 0.000 0.116 0.000 1.000 hr_mtu -0.304 0.116 -2.610 0.009 Geographically Weighted Regression (GWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AIC Bandwidth used: 63.000 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 58.715 Effective number of parameters (trace(S)): 4.730 Degree of freedom (n - trace(S)): 64.270 Sigma estimate: 0.956 Log-likelihood: -92.338 Degree of Dependency (DoD): 0.797 AIC: 196.136 AICc: 197.374 BIC: 208.937 R2: 0.149 Adj. R2: 0.085 Adj. alpha (95%): 0.021 Adj. critical t value (95%): 2.360 Summary Statistics For GWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept -0.047 0.077 -0.150 -0.069 0.094 hr_mtu -0.274 0.085 -0.434 -0.238 -0.146 ================================================================================ Multiscale Geographically Weighted Regression (MGWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AIC Score of change (SOC) type: Smoothing f Termination criterion for MGWR: 1.0e-05 Number of iterations used: 7 MGWR bandwidths -------------------------------------------------------------------------------- Variable Bandwidth ENP_j Adj t-val(95%) DoD_j Intercept 63.000 2.224 2.335 0.811 hr_mtu 44.000 4.025 2.568 0.671 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 55.452 Effective number of parameters (trace(S)): 6.248 Degree of freedom (n - trace(S)): 62.752 Sigma estimate: 0.940 Log-likelihood: -90.366 Degree of Dependency (DoD): 0.731 AIC: 195.228 AICc: 197.197 BIC: 211.422 R2: 0.196 Adj. R2: 0.115 Summary Statistics For MGWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept -0.070 0.057 -0.155 -0.077 0.041 hr_mtu -0.296 0.167 -0.619 -0.288 0.063 ================================================================================ ################################################################################ 09.12.2020 ================================================================================ Model type: Gaussian Number of observations: 69 Number of covariates: 2 Dependent variable: case1209 Variable standardization: On Total runtime: 0:00:00 Global Regression Results -------------------------------------------------------------------------------- Residual sum of squares: 55.519 Log-likelihood: -90.407 AIC: 184.815 AICc: 187.184 R2: 0.195 Adj. R2: 0.183 Variable Est. SE t(Est/SE) p-value ------------------------------------ ---------- ---------- ---------- ---------- Intercept 0.000 0.110 0.000 1.000 hr_mtu -0.442 0.110 -4.033 0.000 Geographically Weighted Regression (GWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AIC Bandwidth used: 67.000 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 53.808 Effective number of parameters (trace(S)): 4.109 Degree of freedom (n - trace(S)): 64.891 Sigma estimate: 0.911 Log-likelihood: -89.327 Degree of Dependency (DoD): 0.830 AIC: 188.872 AICc: 189.864 BIC: 200.286 R2: 0.220 Adj. R2: 0.170 Adj. alpha (95%): 0.024 Adj. critical t value (95%): 2.303 Summary Statistics For GWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept -0.032 0.033 -0.091 -0.036 0.040 hr_mtu -0.423 0.054 -0.541 -0.393 -0.355 ================================================================================ Multiscale Geographically Weighted Regression (MGWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AIC Score of change (SOC) type: Smoothing f Termination criterion for MGWR: 1.0e-05 Number of iterations used: 4 MGWR bandwidths -------------------------------------------------------------------------------- Variable Bandwidth ENP_j Adj t-val(95%) DoD_j Intercept 65.000 2.137 2.319 0.821 hr_mtu 67.000 2.162 2.324 0.818 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 53.576 Effective number of parameters (trace(S)): 4.299 Degree of freedom (n - trace(S)): 64.701 Sigma estimate: 0.910 Log-likelihood: -89.178 Degree of Dependency (DoD): 0.819 AIC: 188.954 AICc: 190.019 BIC: 200.793 R2: 0.224 Adj. R2: 0.171 Summary Statistics For MGWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept -0.038 0.039 -0.101 -0.044 0.048 hr_mtu -0.423 0.055 -0.539 -0.391 -0.360 ================================================================================ ################################################################################ 23.12.2020 ================================================================================ Model type: Gaussian Number of observations: 69 Number of covariates: 3 Dependent variable: case1223 Variable standardization: On Total runtime: 0:00:00 Global Regression Results -------------------------------------------------------------------------------- Residual sum of squares: 57.811 Log-likelihood: -91.803 AIC: 189.606 AICc: 192.231 R2: 0.162 Adj. R2: 0.137 Variable Est. SE t(Est/SE) p-value ------------------------------------ ---------- ---------- ---------- ---------- Intercept 0.000 0.113 0.000 1.000 hr_mtu -0.247 0.128 -1.930 0.054 ulkoka19 0.221 0.128 1.729 0.084 Geographically Weighted Regression (GWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AIC Bandwidth used: 68.000 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 56.262 Effective number of parameters (trace(S)): 5.580 Degree of freedom (n - trace(S)): 63.420 Sigma estimate: 0.942 Log-likelihood: -90.866 Degree of Dependency (DoD): 0.853 AIC: 194.893 AICc: 196.517 BIC: 209.594 R2: 0.185 Adj. R2: 0.112 Adj. alpha (95%): 0.027 Adj. critical t value (95%): 2.262 Summary Statistics For GWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept -0.001 0.021 -0.032 0.007 0.026 hr_mtu -0.214 0.040 -0.303 -0.208 -0.144 ulkoka19 0.308 0.068 0.188 0.327 0.416 ================================================================================ Multiscale Geographically Weighted Regression (MGWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AICc Score of change (SOC) type: Smoothing f Termination criterion for MGWR: 1.0e-05 Number of iterations used: 5 MGWR bandwidths -------------------------------------------------------------------------------- Variable Bandwidth ENP_j Adj t-val(95%) DoD_j Intercept 67.000 1.975 2.287 0.839 hr_mtu 67.000 2.052 2.303 0.830 ulkoka19 67.000 1.800 2.249 0.861 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 56.348 Effective number of parameters (trace(S)): 5.826 Degree of freedom (n - trace(S)): 63.174 Sigma estimate: 0.944 Log-likelihood: -90.918 Degree of Dependency (DoD): 0.843 AIC: 195.489 AICc: 197.236 BIC: 210.740 R2: 0.183 Adj. R2: 0.107 Summary Statistics For MGWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept 0.009 0.019 -0.019 0.007 0.040 hr_mtu -0.229 0.027 -0.292 -0.227 -0.185 ulkoka19 0.304 0.068 0.197 0.312 0.409 ================================================================================ ################################################################################ 13.01.2021 ================================================================================ Model type: Gaussian Number of observations: 69 Number of covariates: 3 Dependent variable: case0113 Variable standardization: On Total runtime: 0:00:00 Global Regression Results -------------------------------------------------------------------------------- Residual sum of squares: 62.918 Log-likelihood: -94.723 AIC: 195.446 AICc: 198.071 R2: 0.088 Adj. R2: 0.061 Variable Est. SE t(Est/SE) p-value ------------------------------------ ---------- ---------- ---------- ---------- Intercept 0.000 0.118 0.000 1.000 ko_perus -0.902 0.433 -2.080 0.037 ulkoka19 1.036 0.433 2.391 0.017 Geographically Weighted Regression (GWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AIC Bandwidth used: 68.000 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 60.791 Effective number of parameters (trace(S)): 5.500 Degree of freedom (n - trace(S)): 63.500 Sigma estimate: 0.978 Log-likelihood: -93.537 Degree of Dependency (DoD): 0.857 AIC: 200.073 AICc: 201.659 BIC: 214.594 R2: 0.119 Adj. R2: 0.041 Adj. alpha (95%): 0.027 Adj. critical t value (95%): 2.256 Summary Statistics For GWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept 0.047 0.039 -0.019 0.046 0.112 ko_perus -0.864 0.208 -1.168 -0.880 -0.516 ulkoka19 1.009 0.213 0.623 1.073 1.280 ================================================================================ Multiscale Geographically Weighted Regression (MGWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AIC Score of change (SOC) type: Smoothing f Termination criterion for MGWR: 1.0e-05 Number of iterations used: 88 MGWR bandwidths -------------------------------------------------------------------------------- Variable Bandwidth ENP_j Adj t-val(95%) DoD_j Intercept 54.000 2.916 2.444 0.747 ko_perus 67.000 1.641 2.210 0.883 ulkoka19 67.000 1.700 2.225 0.875 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 59.686 Effective number of parameters (trace(S)): 6.258 Degree of freedom (n - trace(S)): 62.742 Sigma estimate: 0.975 Log-likelihood: -92.904 Degree of Dependency (DoD): 0.826 AIC: 200.323 AICc: 202.297 BIC: 216.537 R2: 0.135 Adj. R2: 0.047 Summary Statistics For MGWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept 0.078 0.074 -0.044 0.067 0.245 ko_perus -1.042 0.045 -1.125 -1.023 -0.979 ulkoka19 1.220 0.032 1.165 1.212 1.282 ================================================================================ ################################################################################ 27.01.2021 ================================================================================ Model type: Gaussian Number of observations: 69 Number of covariates: 2 Dependent variable: case0127 Variable standardization: On Total runtime: 0:00:00 Global Regression Results -------------------------------------------------------------------------------- Residual sum of squares: 64.804 Log-likelihood: -95.742 AIC: 195.484 AICc: 197.854 R2: 0.061 Adj. R2: 0.047 Variable Est. SE t(Est/SE) p-value ------------------------------------ ---------- ---------- ---------- ---------- Intercept 0.000 0.118 0.000 1.000 hr_mtu -0.247 0.118 -2.083 0.037 Geographically Weighted Regression (GWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AIC Bandwidth used: 67.000 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 60.484 Effective number of parameters (trace(S)): 4.109 Degree of freedom (n - trace(S)): 64.891 Sigma estimate: 0.965 Log-likelihood: -93.362 Degree of Dependency (DoD): 0.830 AIC: 196.942 AICc: 197.935 BIC: 208.356 R2: 0.123 Adj. R2: 0.067 Adj. alpha (95%): 0.024 Adj. critical t value (95%): 2.303 Summary Statistics For GWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept -0.052 0.080 -0.183 -0.062 0.096 hr_mtu -0.230 0.087 -0.408 -0.211 -0.083 ================================================================================ Acknowledgement: We acknowledge the support of the National Science Foundation under Award 1758786 from the Geography and Spatial Sciences Program to A. S. Fotheringham which enabled this software to be written and made freely available. ================================================================================ Multiscale Geographically Weighted Regression (MGWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AIC Score of change (SOC) type: Smoothing f Termination criterion for MGWR: 1.0e-05 Number of iterations used: 6 MGWR bandwidths -------------------------------------------------------------------------------- Variable Bandwidth ENP_j Adj t-val(95%) DoD_j Intercept 67.000 1.964 2.285 0.841 hr_mtu 50.000 3.526 2.518 0.702 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 57.885 Effective number of parameters (trace(S)): 5.490 Degree of freedom (n - trace(S)): 63.510 Sigma estimate: 0.955 Log-likelihood: -91.847 Degree of Dependency (DoD): 0.762 AIC: 196.674 AICc: 198.254 BIC: 211.174 R2: 0.161 Adj. R2: 0.087 Summary Statistics For MGWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept -0.065 0.074 -0.196 -0.066 0.070 hr_mtu -0.232 0.155 -0.624 -0.172 -0.032 ================================================================================ ################################################################################ 10.02.2021 ================================================================================ Model type: Gaussian Number of observations: 69 Number of covariates: 4 Dependent variable: case0210 Variable standardization: On Total runtime: 0:00:00 Global Regression Results -------------------------------------------------------------------------------- Residual sum of squares: 57.268 Log-likelihood: -91.477 AIC: 190.954 AICc: 193.907 R2: 0.170 Adj. R2: 0.132 Variable Est. SE t(Est/SE) p-value ------------------------------------ ---------- ---------- ---------- ---------- Intercept 0.000 0.113 0.000 1.000 hr_mtu -0.250 0.130 -1.920 0.055 pt_tyott 0.981 0.357 2.746 0.006 tr_pi_tul -0.927 0.358 -2.589 0.010 Geographically Weighted Regression (GWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AIC Bandwidth used: 62.000 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 50.510 Effective number of parameters (trace(S)): 8.504 Degree of freedom (n - trace(S)): 60.496 Sigma estimate: 0.914 Log-likelihood: -87.145 Degree of Dependency (DoD): 0.822 AIC: 193.298 AICc: 196.711 BIC: 214.531 R2: 0.268 Adj. R2: 0.163 Adj. alpha (95%): 0.024 Adj. critical t value (95%): 2.317 Summary Statistics For GWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept 0.078 0.082 -0.104 0.099 0.198 hr_mtu -0.203 0.095 -0.370 -0.209 -0.041 pt_tyott 1.215 0.405 0.469 1.315 1.744 tr_pi_tul -1.114 0.397 -1.598 -1.270 -0.322 ================================================================================ Multiscale Geographically Weighted Regression (MGWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AIC Score of change (SOC) type: Smoothing f Termination criterion for MGWR: 1.0e-05 Number of iterations used: 69 MGWR bandwidths -------------------------------------------------------------------------------- Variable Bandwidth ENP_j Adj t-val(95%) DoD_j Intercept 67.000 1.864 2.263 0.853 hr_mtu 67.000 2.036 2.299 0.832 pt_tyott 67.000 1.635 2.208 0.884 tr_pi_tul 67.000 1.623 2.205 0.886 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 53.653 Effective number of parameters (trace(S)): 7.157 Degree of freedom (n - trace(S)): 61.843 Sigma estimate: 0.931 Log-likelihood: -89.228 Degree of Dependency (DoD): 0.863 AIC: 194.770 AICc: 197.266 BIC: 212.994 R2: 0.222 Adj. R2: 0.131 Summary Statistics For MGWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept 0.021 0.058 -0.116 0.027 0.096 hr_mtu -0.225 0.068 -0.355 -0.222 -0.119 pt_tyott 0.961 0.009 0.944 0.963 0.981 tr_pi_tul -0.943 0.056 -1.006 -0.968 -0.848 ================================================================================ ################################################################################ 24.02.2021 ================================================================================ Model type: Gaussian Number of observations: 69 Number of covariates: 4 Dependent variable: case0224 Variable standardization: On Total runtime: 0:00:00 Global Regression Results -------------------------------------------------------------------------------- Residual sum of squares: 46.865 Log-likelihood: -84.561 AIC: 177.121 AICc: 180.074 R2: 0.321 Adj. R2: 0.289 Variable Est. SE t(Est/SE) p-value ------------------------------------ ---------- ---------- ---------- ---------- Intercept -0.000 0.102 -0.000 1.000 ko_perus 1.616 0.454 3.558 0.000 pt_elakel -0.579 0.216 -2.688 0.007 ulkoka19 -0.655 0.383 -1.710 0.087 Geographically Weighted Regression (GWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AIC Bandwidth used: 53.000 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 31.392 Effective number of parameters (trace(S)): 11.088 Degree of freedom (n - trace(S)): 57.912 Sigma estimate: 0.736 Log-likelihood: -70.736 Degree of Dependency (DoD): 0.759 AIC: 165.648 AICc: 171.307 BIC: 192.654 R2: 0.545 Adj. R2: 0.456 Adj. alpha (95%): 0.018 Adj. critical t value (95%): 2.424 Summary Statistics For GWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept -0.101 0.208 -0.378 -0.147 0.319 ko_perus 1.339 0.989 0.291 0.990 3.660 pt_elakel -0.704 0.508 -2.210 -0.559 -0.167 ulkoka19 -0.241 0.760 -1.561 -0.027 0.776 ================================================================================ Multiscale Geographically Weighted Regression (MGWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AIC Score of change (SOC) type: Smoothing f Termination criterion for MGWR: 1.0e-05 Number of iterations used: 171 MGWR bandwidths -------------------------------------------------------------------------------- Variable Bandwidth ENP_j Adj t-val(95%) DoD_j Intercept 53.000 2.872 2.437 0.751 ko_perus 67.000 1.485 2.168 0.907 pt_elakel 63.000 1.887 2.268 0.850 ulkoka19 63.000 1.899 2.271 0.849 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 35.240 Effective number of parameters (trace(S)): 8.143 Degree of freedom (n - trace(S)): 60.857 Sigma estimate: 0.761 Log-likelihood: -74.725 Degree of Dependency (DoD): 0.832 AIC: 167.736 AICc: 170.887 BIC: 188.162 R2: 0.489 Adj. R2: 0.420 Summary Statistics For MGWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept -0.026 0.231 -0.312 -0.109 0.387 ko_perus 1.586 0.039 1.548 1.565 1.672 pt_elakel -0.648 0.104 -0.856 -0.612 -0.516 ulkoka19 -0.554 0.108 -0.725 -0.542 -0.405 ================================================================================ ################################################################################ 10.03.2021 ================================================================================ Model type: Gaussian Number of observations: 69 Number of covariates: 5 Dependent variable: case0310 Variable standardization: On Total runtime: 0:00:00 Global Regression Results -------------------------------------------------------------------------------- Residual sum of squares: 29.383 Log-likelihood: -68.454 AIC: 146.908 AICc: 150.263 R2: 0.574 Adj. R2: 0.548 Variable Est. SE t(Est/SE) p-value ------------------------------------ ---------- ---------- ---------- ---------- Intercept 0.000 0.082 0.000 1.000 hr_mtu -0.324 0.098 -3.306 0.001 hr_pi_tul -0.926 0.254 -3.642 0.000 pt_tyott 0.615 0.300 2.048 0.041 ulkoka19 0.689 0.211 3.270 0.001 Geographically Weighted Regression (GWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AIC Bandwidth used: 66.000 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 24.358 Effective number of parameters (trace(S)): 9.196 Degree of freedom (n - trace(S)): 59.804 Sigma estimate: 0.638 Log-likelihood: -61.983 Degree of Dependency (DoD): 0.856 AIC: 144.359 AICc: 148.309 BIC: 167.139 R2: 0.647 Adj. R2: 0.592 Adj. alpha (95%): 0.027 Adj. critical t value (95%): 2.258 Summary Statistics For GWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept -0.031 0.103 -0.204 -0.035 0.162 hr_mtu -0.294 0.066 -0.432 -0.292 -0.187 hr_pi_tul -0.785 0.123 -1.049 -0.767 -0.585 pt_tyott 0.434 0.064 0.330 0.423 0.601 ulkoka19 0.712 0.089 0.541 0.724 0.842 ================================================================================ Acknowledgement: We acknowledge the support of the National Science Foundation under Award 1758786 from the Geography and Spatial Sciences Program to A. S. Fotheringham which enabled this software to be written and made freely available. ================================================================================ Multiscale Geographically Weighted Regression (MGWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AIC Score of change (SOC) type: Smoothing f Termination criterion for MGWR: 1.0e-05 Number of iterations used: 80 MGWR bandwidths -------------------------------------------------------------------------------- Variable Bandwidth ENP_j Adj t-val(95%) DoD_j Intercept 46.000 3.404 2.504 0.711 hr_mtu 63.000 2.278 2.345 0.806 hr_pi_tul 67.000 1.547 2.185 0.897 pt_tyott 67.000 1.475 2.165 0.908 ulkoka19 67.000 1.527 2.180 0.900 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 22.584 Effective number of parameters (trace(S)): 10.230 Degree of freedom (n - trace(S)): 58.770 Sigma estimate: 0.620 Log-likelihood: -59.375 Degree of Dependency (DoD): 0.831 AIC: 141.211 AICc: 146.050 BIC: 166.301 R2: 0.673 Adj. R2: 0.615 Summary Statistics For MGWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept -0.022 0.166 -0.329 -0.007 0.267 hr_mtu -0.341 0.078 -0.483 -0.348 -0.212 hr_pi_tul -0.727 0.010 -0.742 -0.727 -0.705 pt_tyott 0.312 0.013 0.292 0.308 0.332 ulkoka19 0.740 0.023 0.685 0.741 0.771 ================================================================================ ################################################################################ 24.03.2021 ================================================================================ Model type: Gaussian Number of observations: 69 Number of covariates: 4 Dependent variable: case0324 Variable standardization: On Total runtime: 0:00:00 Global Regression Results -------------------------------------------------------------------------------- Residual sum of squares: 33.685 Log-likelihood: -73.169 AIC: 154.337 AICc: 157.289 R2: 0.512 Adj. R2: 0.489 Variable Est. SE t(Est/SE) p-value ------------------------------------ ---------- ---------- ---------- ---------- Intercept -0.000 0.087 -0.000 1.000 hr_mtu -0.509 0.102 -4.970 0.000 ko_perus -0.493 0.296 -1.668 0.095 pt_tyott 0.792 0.287 2.755 0.006 Geographically Weighted Regression (GWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AIC Bandwidth used: 56.000 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 26.799 Effective number of parameters (trace(S)): 9.875 Degree of freedom (n - trace(S)): 59.125 Sigma estimate: 0.673 Log-likelihood: -65.279 Degree of Dependency (DoD): 0.787 AIC: 152.309 AICc: 156.830 BIC: 176.605 R2: 0.612 Adj. R2: 0.546 Adj. alpha (95%): 0.020 Adj. critical t value (95%): 2.377 Summary Statistics For GWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept -0.136 0.125 -0.291 -0.193 0.170 hr_mtu -0.537 0.084 -0.716 -0.502 -0.426 ko_perus -0.840 0.527 -1.908 -0.711 -0.201 pt_tyott 0.933 0.309 0.452 0.970 1.476 ================================================================================ Multiscale Geographically Weighted Regression (MGWR) Results -------------------------------------------------------------------------------- Coordinates type: Projected Spatial kernel: Adaptive bisquare Criterion for optimal bandwidth: AIC Score of change (SOC) type: Smoothing f Termination criterion for MGWR: 1.0e-05 Number of iterations used: 88 MGWR bandwidths -------------------------------------------------------------------------------- Variable Bandwidth ENP_j Adj t-val(95%) DoD_j Intercept 44.000 3.578 2.523 0.699 hr_mtu 67.000 1.969 2.286 0.840 ko_perus 61.000 1.928 2.277 0.845 pt_tyott 67.000 1.549 2.186 0.897 Diagnostic Information -------------------------------------------------------------------------------- Residual sum of squares: 25.695 Effective number of parameters (trace(S)): 9.025 Degree of freedom (n - trace(S)): 59.975 Sigma estimate: 0.655 Log-likelihood: -63.828 Degree of Dependency (DoD): 0.808 AIC: 147.705 AICc: 151.517 BIC: 170.101 R2: 0.628 Adj. R2: 0.571 Summary Statistics For MGWR Parameter Estimates -------------------------------------------------------------------------------- Variable Mean STD Min Median Max -------------------- ---------- ---------- ---------- ---------- ---------- Intercept -0.070 0.156 -0.336 -0.043 0.154 hr_mtu -0.561 0.058 -0.686 -0.536 -0.496 ko_perus -0.476 0.096 -0.678 -0.442 -0.365 pt_tyott 0.644 0.019 0.602 0.652 0.675 ================================================================================ ################################################################################