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. 2023 Jun 5;13:9065. doi: 10.1038/s41598-023-36106-3

Table 3.

Models for PET levels on signal timing.

Yellow time
Random parameters ordered logit models Random parameters ordered logit model with heterogeneity in means
Coefficients: Estimate Odds ratio Std. error z-value Pr( >|z|) Coefficients: Estimate Odds ratio SE z-value Pr( >|z|)
No. of Obs = 2955, Log Likelihood = − 3667, AIC = 7361, BIC = 7445 No. of Obs = 2955, Log Likelihood = − 3658, AIC = 7351, BIC = 7459
Constant 4.685 – 0.884 5.301 0*** Constant 4.603 0.824 5.584 0.000***
Distance − 0.175 0.839 0.048 − 3.661 0*** Distance − 0.198 0.820 0.050 − 3.979 0.000***
Yellow 0.151 1.163 0.035 4.359 0*** Mean: yellow 0.104 1.109 0.043 2.434 0.015*
SD: yellow 0.363 1.437 0.031 11.528 0.000***
Phase 3 0.728 2.071 0.321 2.269 0.023* Phase 3 1.257 3.513 0.299 4.196 0.000***
Phase 5 − 0.897 0.408 0.474 − 1.893 0.058 Phase 5 − 0.461 0.631 0.337 − 1.367 0.172
Phase 6 2.004 7.416 0.55 3.641 0*** Phase 6 3.262 26.093 0.808 4.035 0.000***
Phase 7 1.444 4.238 0.288 5.022 0*** Phase 7 1.650 5.205 0.362 4.552 0.000***
Phase 8 2.032 7.628 1.005 2.022 0.043* Phase 8 2.190 8.940 0.733 2.989 0.003**
Mean. volume 0.01 1.01 0.013 0.745 0.456 Mean. volume 0.022 1.023 0.013 1.782 0.075
SD volume 0.056 1.058 0.003 18.97 0*** SD volume 0.051 1.052 0.002 24.037 0.000***
Heterogeneity in mean: volume * yellow − 0.001 0.999 0.002 − 0.707 0.480
Kappa.1 3.853 – 0.117 32.892 0*** Kappa.1 3.862 – 0.115 33.700 0.000***
Kappa.2 5.298 – 0.13 40.651 0*** Kappa.2 5.339 – 0.130 41.144 0.000***
Kappa.3 7.004 – 0.15 46.577 0*** Kappa.3 7.080 – 0.151 46.880 0.000***
All red time
No. of Obs = 805, Log Likelihood = − 683.8, AIC = 1399.564, BIC = 1474.618 No. of Obs = 805, Log Likelihood = − 651.1, AIC = 1342, BIC = 1435
Constant 14.475 – 1.162 12.451 0*** Constant 13.571 1.199 11.319 0.000***
Speeding prop 3.956 52.274 0.732 5.404 0*** Speeding_prop 5.040 154.526 0.563 8.949 0.000***
All red − 0.558 0.572 0.124 − 4.515 0*** Mean. all_red 0.172 1.188 0.129 1.333 0.183
SD. all_red 1.252 3.496 0.111 11.285 0.000***
Distance 0.111 1.117 0.054 2.044 0.041*
Phase 1 − 2.573 0.076 0.57 − 4.514 0*** Phase 1 − 1.843 0.158 0.568 − 3.244 0.001**
Phase 2 3.644 38.238 0.605 6.027 0*** Phase 2 1.792 6.001 0.410 4.374 0.000***
Phase 3 − 1.262 0.283 0.573 − 2.202 0.028* Phase 3 − 2.431 0.088 0.482 − 5.040 0.000***
Phase 4 4.986 146.288 1.332 3.743 0*** Phase 4 1.133 3.105 0.944 1.200 0.230
Phase 5 4.196 66.43 1.122 3.739 0*** Phase 5 1.593 4.917 0.598 2.665 0.008**
Phase 7 4.058 57.855 0.861 4.711 0*** Phase 8 − 2.607 0.074 1.067 − 2.444 0.015*
Mean. volume − 0.089 0.915 0.018 − 5.022 0*** Volume − 0.074 0.929 0.013 − 5.742 0.000***
SD volume 0.117 1.124 0.007 15.714 0*** mean. intersection 7.445 1711.371 1.370 5.435 0.000***
SD intersection 4.824 124.454 0.322 14.999 0.000***
Heterogeneity in mean: intersection.all_red − 2.648 0.071 0.396 − 6.684 0.000***
Kappa.1 4.96 – 0.438 11.316 0*** Kappa.1 5.22277 – 0.44709 11.682 0.000***
Kappa.2 8.259 – 0.515 16.039 0*** Kappa.2 8.71902 – 0.54801 15.91 0.000***
Kappa.3 11.026 – 0.596 18.487 0*** Kappa.3 11.38398 – 0.61409 18.538 0.000***
Red clearance
No. of Obs = 6785, Log Likelihood = − 8881, AIC = 19,792, BIC = 19,915 No. of Obs = 6785, Log Likelihood = − 8956, AIC = 17,952, BIC = 18,088
Constant 8.072 – 0.574 14.058 0*** Constant 7.327 0.418 17.511 0.000***
Speeding prop 0.421 1.523 0.159 2.654 0.008** Speeding_prop 0.156 1.169 0.167 0.933 0.351
Distance − 0.155 0.856 0.023 − 6.672 0*** Distance − 0.158 0.854 0.024 − 6.544 0.000***
Red clearance 0.033 1.033 0.023 1.443 0.149 Mean. red_clearance 0.034 1.034 0.028 1.225 0.220
SD. red_clearance 0.513 1.671 0.021 23.887 0.000***
Intersection − 0.338 0.714 0.084 − 4.003 0*** Mean. intersection 1.825 6.200 0.297 6.138 0.000***
SD. intersection 1.646 5.186 0.091 18.054 0.000***
Phase 1 − 0.701 0.496 0.413 − 1.696 0.09 Phase 1 − 0.618 0.539 0.395 − 1.565 0.118
Phase 2 − 1.03 0.357 0.209 − 4.937 0*** Phase 2 − 0.701 0.496 0.138 − 5.088 0.000***
Phase 3 − 1.821 0.162 0.605 − 3.01 0.003** Phase 3 − 1.437 0.238 1.380 − 1.041 0.298
Phase 4 − 5.175 0.006 0.703 − 7.36 0*** Phase 4 − 4.856 0.008 0.629 − 7.726 0.000***
Phase 5 − 3.126 0.044 0.329 − 9.492 0*** Phase 5 − 2.391 0.092 0.203 − 11.804 0.000***
Phase 6 − 1.471 0.23 0.23 − 6.402 0*** Phase 6 − 0.820 0.441 0.192 − 4.272 0.000***
Phase 7 − 1.488 0.226 0.218 − 6.82 0*** Phase 7 − 1.528 0.217 0.174 − 8.775 0.000***
Phase 8 − 1.106 0.331 0.319 − 3.466 0.001*** Phase 8 − 1.728 0.178 0.389 − 4.447 0.000***
Mean. volume − 0.001 0.999 0.01 − 0.063 0.95 Volume 0.005 1.005 0.004 1.388 0.165
SD volume 0.042 1.043 0.002 25.986 0***
Heterogeneity in mean: intersection.red_clearance − 0.532 0.071 − 7.533 0.000***
Kappa.1 3.514 – 0.083 42.558 0*** Kappa.1 3.456 – 0.080 43.082 0.000***
Kappa.2 4.85 – 0.089 54.498 0*** Kappa.2 4.754 – 0.086 55.066 0.000***
Kappa.3 6.514 – 0.098 66.606 0*** Kappa.3 6.380 – 0.095 67.419 0.000***
Red time
No. of Obs = 7112, Log Likelihood = − 10,150, AIC = 20,334, BIC = 20,451 No. of Obs = 7112, Log Likelihood = − 10,130, AIC = 20,301, BIC = 20,432
Constant 4.198 – 0.222 18.95 0*** Constant 4.982 0.284 17.577 0.000***
Speeding prop 1.398 4.049 0.105 13.264 0*** Speeding_prop 1.471 4.354 0.117 12.545 0.000***
Distance 0.096 1.101 0.011 9.036 0*** Distance 0.104 1.110 0.011 9.114 0.000***
Red − 0.004 0.996 0.001 − 7.579 0*** Mean. red − 0.014 0.986 0.003 − 5.666 0.000***
SD. red 0.007 1.007 0.001 7.238 0.000***
Intersection − 1.043 0.352 0.07 − 14.912 0*** Intersection − 1.101 0.333 0.078 − 14.075 0.000***
Phase 2 0.371 1.45 0.089 4.158 0*** Phase 2 0.429 1.535 0.095 4.531 0.000***
Phase 4 0.639 1.894 0.163 3.921 0*** Phase 4 0.617 1.853 0.176 3.504 0.000***
Phase 5 − 0.245 0.783 0.134 − 1.826 0.068*
Phase 6 0.652 1.92 0.134 4.868 0*** Phase 6 0.769 2.158 0.142 5.432 0.000***
Mean. volume − 0.011 0.989 0.002 − 4.674 0*** Mean. volume − 0.023 0.977 0.004 − 6.216 0.000***
SD volume 0.013 1.013 0.003 4.616 0*** SD volume 0.014 1.015 0.003 4.622 0.000***
Heterogeneity in mean: volume.red 0.0002 1.000 0.000 4.212 0.000***
Kappa.1 2.4 – 0.084 28.496 0*** Kappa.1 2.568 – 0.108 23.883 0.000***
Kappa.2 3.659 – 0.122 30.101 0*** Kappa.2 3.920 – 0.159 24.668 0.000***
Kappa.3 4.859 – 0.157 30.943 0*** Kappa.3 5.197 – 0.206 25.172 0.000***
Green time
No. of Obs = 62,416, Log Likelihood = − 91,730, AIC = 183,497, BIC = 183,651 No. of Obs = 62,416, Log Likelihood = − 91,730, AIC = 183,449, BIC = 183,631
Constant 4.767 – 0.092 51.701 0*** Constant 4.870 0.111 43.990 0.000***
Speeding prop 0.85 2.34 0.033 25.571 0*** Speeding_prop 0.856 2.353 0.033 25.624 0.000***
Distance − 0.082 0.921 0.005 − 14.983 0*** Distance − 0.082 0.921 0.005 − 15.020 0.000***
Green 0.019 1.02 0.001 28.633 0*** Mean. green 0.015 1.015 0.002 6.178 0.000***
SD. green 0.000 1.000 0.001 0.205 0.837
Intersection − 0.272 0.762 0.016 − 16.767 0*** Intersection − 0.273 0.761 0.016 − 16.785 0.000***
Phase 2 − 0.265 0.767 0.027 − 9.951 0*** Phase 2 − 0.254 0.776 0.027 − 9.301 0.000***
Phase 4 − 0.922 0.398 0.05 − 18.607 0*** Phase 4 − 0.897 0.408 0.051 − 17.507 0.000***
Phase 5 0.146 1.157 0.046 3.202 0.001** Phase 5 0.166 1.181 0.047 3.525 0.000***
Phase 6 − 0.641 0.527 0.035 − 18.238 0*** Phase 6 − 0.642 0.526 0.035 − 18.245 0.000***
Phase 7 0.174 1.19 0.032 5.374 0*** Phase 7 0.176 1.193 0.032 5.440 0.000***
Phase 8 − 0.606 0.546 0.039 − 15.69 0*** Phase 8 − 0.594 0.552 0.039 − 15.112 0.000***
Mean. volume − 0.001 0.999 0.001 − 1.206 0.228 Mean. volume − 0.003 0.997 0.001 − 2.037 0.042*
SD volume 0.006 1.006 0.001 4.394 0*** SD volume 0.006 1.006 0.001 4.484 0.000***
Heterogeneity in mean: volume. green 0.0001 1.000 0.000 1.665 0.096
Kappa.1 2.511 – 0.024 103.157 0*** Kappa.1 2.512 – 0.024 102.981 0.000***
Kappa.2 3.531 – 0.032 110.856 0*** Kappa.2 3.533 – 0.032 110.595 0.000***
Kappa.3 4.712 – 0.041 115.072 0*** Kappa.3 4.715 – 0.041 114.763 0.000***