Do Expressway Interchanges Increase Crash Injury Severities? Insights Using Temporal Instability and Unobserved Heterogeneity
Table 10
The results of IAC and NIAC models based on random parameter logit model with heterogeneity in mean and variance.
Variable
2017
2018
2019
2017–20191
IAC
NIAC
IAC
NIAC
IAC
NIAC
IAC
NIAC
[MI]2 constant
−0.251 (−2.98)
−1.206 (−4.40)
−1.655 (−2.91)
−2.451 (−5.07)
3.462 (2.72)
−2.803 (−2.81)
−0.853 (−2.66)
1.561 (4.00)
[SI] constant
−6.256 (−2.75)
−3.103 (−2.25)
−5.501 (−5.51)
−1.667 (−2.89)
−6.632 (−4.59)
−5.73 (−7.36)
−4.425 (−6.94)
−0.306 (−3.45)
Driver characteristics
[MI] improper action (1 if improper action, 0 otherwise)
−0.626 (−2.82)
−3.511 (−3.67)
Vehicle characteristics
[NI] single-vehicle indicator (1 if the number of vehicles involved in the crash is 1, 0 otherwise)
2.516 (4.15)
[SI] single-vehicle indicator (1 if the number of vehicles involved in the crash is 1, 0 otherwise)
−1.037 (−2.16)
−0.803 (−2.90)
[MI] two-vehicle indicator (1 if the number of vehicles involved in the crash is 2, 0 otherwise)
−1.100 (−3.60)
[NI] multivehicle indicator (1: the total number of vehicles in the crash is more than 2, otherwise 0)
−0.957 (−2.83)
−1.489 (−2.00)
[MI] multivehicle indicator (1: the total number of vehicles in the crash is more than 2, otherwise 0)
1.136 (3.93)
1.813 (2.93)
[SI] multivehicle indicator (1: the total number of vehicles in the crash is more than 2, otherwise 0)
3.201 (2.57)
1.391 (2.62)
[SI] passenger car (1 if the passenger car involved in crash, otherwise 0)
−0.323 (−2.59)
[MI] minibus (1 if the van involved in crash, otherwise 0)
1.304 (2.51)
[NI] bus (1 if the bus involved in crash, otherwise 0)
−0.818 (−2.90)
[NI] van (1 if the minibus involved in crash, otherwise 0)
−1.934 (−1.98)
[SI] van (1 if the minibus involved in crash, otherwise 0)
1.295 (2.59)
[MI] truck (1 if the truck involved in crash, otherwise 0)
1.591 (2.00)
[SI] truck (1 if the truck involved in crash, otherwise 0)
1.478 (2.12)
−1.986 (−2.79)
−0.996 (−2.48)
[MI] heavy truck (1 if the heavy truck involved in crash, otherwise 0)
0.556 (2.45)
0.846 (2.56)
Road characteristics
[SI] : radius of the horizontal curve (103 m)
0.00150 (2.11)
0.00065 (2.59)
[SI] radius of the plane curve of back section (103 m)
0.00126 (2.30)
[NI] : length of the horizontal curve (103 m)
−0.404 (−2.73)
[MI] : length of the horizontal curve (103 m)
0.374 (2.24)
0.125 (2.73)
[SI] : length of the longitudinal slope corresponding to the minimum grade (m)
−0.00103 (−2.03)
[MI] : length of the longitudinal slope corresponding to the maximum grade (m)
−0.00116 (−2.71)
−0.00167 (−2.58)
[NI] : maximum longitudinal grade of current section (%)
0.00383 (2.90)
Environmental characteristics
[MI] fine weather (1 if weather condition is fine, 0 otherwise)
−0.920 (−2.74)
[SI] fine weather (1 if weather condition is fine, 0 otherwise)
1.069 (2.18)
[MI] cloudy weather (1 if weather condition is cloudy, 0 otherwise)
0.697 (2.97)
[MI] rainy weather (1 if weather condition is rainy, 0 otherwise)
−1.165 (−2.91)
[SI] rainy weather (1 if weather condition is rainy, 0 otherwise)
1.813 (2.28)
[MI] snowy weather (1 if weather condition is snowy, 0 otherwise)
0.829 (2.33)
[NI] icy surface condition (1 if surface condition is icy, 0 otherwise)
1.561 (4.00)
[SI] icy surface condition (1 if surface condition is icy, 0 otherwise)
0.550 (2.16)
Temporal characteristics
[SI] Monday (1: occurs on Monday, otherwise 0)
1.590 (3.53)
0.647 (2.04)
[NI] Tuesday (1: occurs on Tuesday, otherwise 0)
−1.591 (−2.45)
[MI] Tuesday (1: occurs on Tuesday, otherwise 0)
1.438 (2.57)
[SI] Tuesday (1: occurs on Tuesday, otherwise 0)
2.527 (2.03)
[SI] Wednesday (1: occurs on Wednesday, otherwise 0)
1.187 (2.63)
1.050 (2.57)
1.639 (2.20)
[SI] early morning (1: occurs from 0 : 00 to 5 : 59, otherwise 0)
1.191 (2.14)
3.105 (3.39)
1.071 (2.92)
2.568 (3.78)
0.865 (3.25)
[MI] afternoon (1: occurs from 12 : 00 to 17 : 59, otherwise 0)
−0.574 (−2.73)
−0.662 (−2.43)
[SI] afternoon (1: occurs from 12 : 00 to 17 : 59, otherwise 0)
−0.692 (−2.77)
[MI] night (1: occurs from 18 : 00–23 : 59, otherwise 0)
−0.627 (−2.06)
[SI] night (1: occurs from 18 : 00–23 : 59, otherwise 0)
1.548 (2.88)
1.920 (2.59)
2.258 (2.40)
1.497 (2.06)
[NI] spring (1: occurs in spring, otherwise, 0)
0.431 (2.50)
[SI] spring (1: occurs in spring, otherwise, 0)
1.642 (2.53)
[MI] summer (1: occurs in summer, otherwise 0)
0.530 (2.29)
0.362 (2.34)
[NI] winter (1: occurs in winter, otherwise 0)
−2.094 (−2.98)
−0.393 (−2.78)
−1.829 (−2.33)
[SI] winter (1: occurs in winter, otherwise 0)
0.732 (2.76)
1.479 (2.20)
0.551 (2.89)
Traffic characteristics
[SI] bridge (1: the section occurring is the bridge section, otherwise 0)
−1.847 (−2.26)
[MI] AADT (annual mean daily traffic volume, pcu/d)
−0.000759 (−2.88)
−0.000604 (−2.68)
−0.000210 (−2.51)
−0.000448 (−2.77)
−0.000600 (−2.12)
[SI] AADT (annual mean daily traffic volume, pcu/d)
−0.000535 (−3.55)
−0.000402 (−3.67)
Crash characteristics
[NI] sideswipe (1: the crash type is sideswipe, otherwise 0)
−3.649 (−4.14)
[SI] sideswipe (1: the crash type is sideswipe, otherwise 0)
2.941 (2.55)
[SI] hit fixed object (1: the crash type is hitting fixed object, otherwise 0)
−1.894 (−2.11)
[MI] running off the road (1: the crash type is running off the road, otherwise 0)
1.016 (2.15)
[MI] rollover (1: the crash type is rollover, otherwise 0)
1.048 (3.30)
[SI] rear-end collision (1: the crash type is rear-end collision, otherwise 0)
−0.523 (−2.60)
[MI] other crash types (1: other crash types, otherwise 0)
−0.781 (−2.94)
1.440 (2.61)
[SI] EMS greater than 60 minutes (1: rescue response time greater than 60 minutes, otherwise 0)
0.959 (2.45)
Random parameter (normally distributed)
[MI] over speed (1: the driver is speeding, otherwise 0)
−3.286 (−2.97)
Standard deviation
1.381 (2.20)
[SI] single-vehicle indicator (1 if the number of vehicles involved in the crash is 1, 0 otherwise)
−6.502 (−2.89)
Standard deviation
4.809 (2.22)
[SI] AADT (annual mean daily traffic volume, pcu/d)
−0.000926 (−2.22)
Standard deviation
0.318 (2.63)
[SI] : length of the longitudinal slope corresponding to the minimum grade (m)
−0.00463 (−1.98)
Standard deviation
0.00215 (2.31)
[MI] other crash types (1: other crash types, otherwise 0)
−3.244 (−2.12)
Standard deviation
3.794 (3.35)
Heterogeneity of random parameter mean
[MI] over speed (1: the driver is speeding, otherwise 0): Sunday (1: occurred on Sunday)
−1.233 (−2.66)
[SI] single-vehicle indicator (1 if the number of vehicles involved in the crash is 1, 0 otherwise): Tuesday (1: occurs on Tuesday)
4.707 (2.95)
[SI] : length of the longitudinal slope corresponding to the minimum grade (m): early morning (1: occurs from 0 : 00 to 5 : 59, otherwise 0)
0.00215 (2.88)
[MI] other crash types (1: other crash types, otherwise 0): early morning (1: occurs from 0 : 00 to 5 : 59, otherwise 0)
3.794 (3.35)
Heterogeneity of random parameter variance
[SI] single-vehicle indicator (1 if the number of vehicles involved in the crash is 1, 0 otherwise): afternoon (1: occurs from 12 : 00 to 17 : 59)
−0.343 (−2.67)
Number of parameters (K)
6
20
10
22
6
15
14
27
Number of observations (N)
224
1399
209
1675
197
1500
630
4574
Log-likelihood at zero ()
−245.952
−1536.102
−229.482
−1839.15
−216.306
−1647.304
−691.74
−5022.252
Log-likelihood at convergence ()
−56.711
−499.365
−74.762
−569.698
−72.348
−477.469
−129.161
−1261.398
0.769
0.675
0.674
0.690
0.666
0.710
0.813
0.749
Akaike information criterion (AIC)
125.422
1038.730
169.524
1183.396
156.696
984.938
286.322
2576.796
Bayesian information criterion (BIC)
145.892
1143.600
202.947
1302.715
176.395
1064.636
348.562
2750.356
Note. 1To better explore the structural fracture and temporal variation in the estimated results, the overall combined data of the year 2017–2019 were used as a reference, covering three years of IAC and NIAC, respectively. 2It represents significant effects on MI, where NI represents no injury, MI represents minor injury, and SI represents severe injury.
