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

Table 3

Random-parameter multivariate Poisson 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	0.0432 (0.27)	0.501 (3.17)	−0.527 (−2.11)	−0.0332 (−0.21)	−0.430 (−1.13)
Traffic characteristics
Interchange	3	—^3	—	−0.422 (−2.91)	−0.164 (−1.95)	−0.601 (−2.55)
Black spots	5	0.0986 (1.24)	0.859 (9.77)	1.276 (7.17)	1.196 (9.54)	1.322 (4.88)
AADT	4	1.057 (11.06)	0.00000936 (3.00)	0.0000126 (2.52)	0.0000365 (11.55)	—
Speed characteristics
	5	−0.0131 (−3.63)	−0.00812 (−2.38)	−0.0140 (−2.63)	−0.0177 (−4.58)	−0.016 (−1.85)
	5	0.0114 (3.31)	0.00828 (2.45)	0.0109 (2.09)	0.0119 (3.25)	0.0237 (2.45)
	2	0.0210 (3.14)	—	—	−0.0272 (3.82)	—
	4	−0.0190 (−4.09)	−0.00148 (0.22)	−0.0182 (−2.67)	−0.0221 (−4.40)	—
Geometric characteristics
	1	—	—	—	—	0.000251 (2.13)
	2	0.000000361 (3.69)	—	—	0.000000375 (3.63)	—
	5	0.000588 (10.32)	0.000468 (8.12)	0.000755 (8.09)	0.000753 (11.64)	0.000748 (6.25)
	1	—	−0.000133 (−2.48)	—	—	—
	2	−0.000357 (−2.51)	—	—	−0.000423 (−2.83)	—
Sight characteristics
	5	−0.00540 (−2.78)	−0.00633 (−2.86)	−0.0111 (−3.20)	−0.00706 (−3.44)	−0.0135 (−2.51)
	3	−0.0860 (−2.13)	−0.105 (−2.57)	—	−0.0878 (−2.06)	—

Note: variables not shown here attribute to insignificant. ¹Variable definitions and units can be seen in Table 2. ²Number of parameters estimated. ³Insignificant at the 95% significance level. Total number of parameters: 52; log-likelihood: −14353.079; AIC: 28996.159; BIC: 29567.814; : 21264.957.