Random-Parameter Multivariate Negative Binomial Regression for Modeling Impacts of Contributing Factors on the Crash Frequency by Crash Types

Table 7

Independent negative binomial model estimation results.

Variables^1	No.^2	Rear-end estimate (t-stat)	Bumping-guardrail estimate (t-stat)	Other estimate (t-stat)	Noncasualty estimate (t-stat)	Casualty estimate (t-stat)
Constant	5	0.043 (0.27)	0.502 (3.07)	−0.528 (−2.11)	−0.033 (−0.21)	−0.431 (−1.13)
Traffic characteristics
Interchange	3	—^3	—	−0.422 (−2.91)	−0.165 (−1.95)	−0.601 (−2.55)
Black spots	5	1.057 (11.06)	0.859 (9.77)	1.276 (7.17)	1.196 (9.54)	1.322 (4.88)
AADT		0.00003 (8.66)	0.00001 (3.00)	0.00001 (2.52)	0.00004 (11.55)	—
Speed characteristics
	5	−0.013 (−3.63)	−0.008 (−2.38)	−0.014 (−2.63)	−0.017 (−4.58)	−0.016 (−1.85)
	5	0.011 (3.31)	0.008 (2.45)	0.010 (2.09)	0.011 (3.25)	0.023 (0.014)
	2	0.021 (3.14)	—	—	0.027 (3.82)	—
	4	−0.019 (−4.09)	−0.009 (−2.11)	−0.018 (−2.67)	−0.022 (−4.40)	—
Geometric characteristics
	1	—	—	—	—	0.000251 (2.13)
	2	0.00000036 (3.63)	—	—	0.000000379 (3.60)	—
	5	0.0005888 (10.28)	0.0004658 (8.04)	0.0007505 (8.02)	0.0007521 (11.57)	0.000750 (6.23)
	1	—	−0.0001341 (−2.49)	—	—	—
	4	−0.000356 (−2.5)	—	−0.0004069 (−1.88)	−0.0004248 (−2.83)	−0.000586 (−1.76)
Sight characteristics
	5	−0.054 (−2.78)	−0.006 (−2.86)	−0.011 (−3.20)	−0.007 (−3.44)	−0.013 (−2.51)
	3	−0.086 (−2.13)	−0.105 (−2.57)	—	−0.087 (−2.06)	—

Note: ¹variable definitions and units can be seen in Table 2. Variables not shown here attribute to insignificant. ²Number of parameters estimated. ³Insignificant at the 95% significance level. Total number of parameters: 55; log-likelihood: −14352.787; AIC: 29007.581; BIC: 29602.802; :21274.146.