Do Expressway Interchanges Increase Crash Injury Severities? Insights Using Temporal Instability and Unobserved Heterogeneity

Table 9

Goodness-of-fit measures among different models.

	Fixed parameter multinomial logit		Random parameter logit		Random parameter logit with heterogeneity in means		Random parameter logit with heterogeneity in means and variances
	IAC	NIAC	IAC	NIAC	IAC	NIAC	IAC	NIAC
2017
Number of parameters (K)	6	19	6	20	6	20	6	20
Number of observations (N)	224	1399	224	1399	224	1399	224	1399
Log-likelihood at zero ()	−245.952	−1536.102	−245.952	−1536.102	−245.952	−1536.102	−245.952	−1536.102
Log-likelihood at convergence ()	−56.711	−503.365	−56.711	−499.365	−56.711	−499.365	−56.711	−499.365
	0.769	0.672	0.769	0.675	0.769	0.675	0.769	0.675
Akaike information criterion (AIC)	125.422	1044.730	125.422	1038.730	125.422	1038.730	125.422	1038.730
Bayesian information criterion (BIC)	145.892	1144.357	145.892	1143.600	145.892	1143.600	145.892	1143.600
2018
Number of parameters (K)	10	19	10	20	10	21	10	22
Number of observations (N)	209	1675	209	1675	209	1675	209	1675
Log-likelihood at zero ()	−229.482	−1839.15	−229.482	−1839.15	−229.482	−1839.15	−229.482	−1839.15
Log-likelihood at convergence ()	−74.762	−594.635	−74.762	−593.254	−74.762	−582.326	−74.762	−569.698
	0.674	0.677	0.674	0.677	0.674	0.683	0.674	0.690
Akaike information criterion (AIC)	169.524	1227.270	169.524	1226.508	169.524	1206.652	169.524	1183.396
Bayesian information criterion (BIC)	202.947	1330.318	202.947	1334.979	202.947	1320.547	202.947	1302.715
2019
Number of parameters (K)	6	13	6	14	6	15	6	15
Number of observations (N)	197	1500	197	1500	197	1500	197	1500
Log-likelihood at zero ()	−216.306	−1647.304	−216.306	−1647.304	−216.306	−1647.304	−216.306	−1647.304
Log-likelihood at convergence ()	−72.348	−484.658	−72.348	−481.264	−72.348	−477.469	−72.348	−477.469
	0.666	0.706	0.666	0.708	0.666	0.710	0.666	0.710
Akaike information criterion (AIC)	156.696	995.316	156.696	990.528	156.696	984.938	156.696	984.938
Bayesian information criterion (BIC)	176.395	1064.388	176.395	1064.913	176.395	1064.636	176.395	1064.636
2017–2019
Number of parameters (K)	14	23	14	25	14	27	14	27
Number of observations (N)	630	4574	630	4574	630	4574	630	4574
Log-likelihood at zero ()	−691.74	−5022.252	−691.74	−5022.252	−691.74	−5022.252	−691.74	−5022.252
Log-likelihood at convergence ()	−129.161	−1275.649	−129.161	−1269.516	−129.161	−1261.398	−129.161	−1261.398
	0.813	0.746	0.813	0.747	0.813	0.749	0.813	0.749
Akaike information criterion (AIC)	286.322	2597.298	286.322	2589.032	286.322	2576.796	286.322	2576.796
Bayesian information criterion (BIC)	348.562	2745.145	348.562	2749.736	348.562	2750.356	348.562	2750.356