Deciphering spatial heterogeneity of maritime accidents considering impact scale variations

Figures & data

Figure 1. The study water area (21°35’ − 27°43’ N and 115°7’ − 125°33’ E) and locations of recorded maritime accidents.

Table 1. Descriptive statistics of the maritime accident characteristics in the Fujian water area.

Variables	Descriptions	Types	Moran’s I
Dependent variable
Accident consequence	The human life loss and property damage cost resulting from maritime accidents ×10^4 CNY (99.405)	Continuous	0.047
Accident types
Collision	1 = collision (41.3%), 0 = otherwise (58.7%)	Categorical	0.418*
Contact	1 = contact (17.1%), 0 = otherwise (82.9%)	Categorical	0.559*
Striking rock	1 = striking rock (10.8%), 0 = otherwise (89.2%)	Categorical	0.161
Grounding	1 = grounding (10.4%), 0 = otherwise (89.6%)	Categorical	−0.053
Sinking/capsizing	1 = sinking/capsizing (7.4%), 0 = otherwise (92.6%)	Categorical	0.377*
Fire/explosion	1 = fire/explosion (4.5%), 0 = otherwise (95.5%)	Categorical	0.027
Other accident types	1 = other accident types (4.9%), 0 = otherwise (95.1%)	Categorical	−0.001
Ship information
Two dry cargo ship involved	1 = two involved (16.9%), 0 = otherwise (83.1%)	Categorical	0.282*
One dry cargo ship involved	1 = one involved (66.7%), 0 = otherwise (33.3%)	Categorical	0.126
Fishing ship	1 = involved (14.9%), 0 = otherwise (85.1%)	Categorical	0.208
Liquid cargo ship	1 = involved (7.4%), 0 = otherwise (92.6%)	Categorical	0.063
Other ship types	1 = involved (17.9%), 0 = otherwise (82.1%)	Categorical	0.482*
Gross tonnage	The sum of tonnage for ships involved in the accident (5699.626)	Continuous	0.257
Navigational status	1 = underway (82.2%), 0 = moored/docked (17.8%)	Categorical	0.426*
Environmental characteristics
Time of the day	1 = nighttime period (50.6%), 0 = daytime period (49.4%)	Categorical	0.245*
Good visibility	1 = yes (17.4%), 0 = no (82.6%)	Categorical	0.181
Restricted visibility	1 = yes (6.7%), 0 = no (93.3%)	Categorical	0.015
Strong wind/wave	1 = yes (25.5%), 0 = no (74.5%)	Categorical	0.096
Typhoon	1 = yes (4.1%), 0 = no (95.9%)	Categorical	0.032
Accident cause factors
Judgment error	1 = yes (10.5%), 0 = no (89.5%)	Categorical	−0.080
Lookout failure	1 = yes (34.9%), 0 = no (65.1%)	Categorical	0.135
Operation error	1 = yes (55.1%), 0 = no (44.9%)	Categorical	0.011
Machinery failure	1 = yes (7.8%), 0 = no (92.2%)	Categorical	0.352*

The statistics in parentheses: mean values for continuous variables, percentages for categorical variables; Average exchange rate during 2000–2014: 1 CNY=0.13732 USD; *p ≤ 0.05.

Figure 2. Flowchart of methodology.

Figure 3. Heat map for the maritime accidents in Fujian water area: (a) accident frequency; (b) accident consequence.

Table 2. Comparison of the performance of the three models.

Model indicators	MLR	GWR	MGWR
R-Squared	0.178	0.238	0.465
Adjusted R-Squared	0.165	0.203	0.392
AICc	3340.391	3319.915	3102.491
RSS	1026.344	950.624	668.211
Log-likelihood	−1648.818	−1600.996	−1381.026
Moran’s I in residual	0.046	0.025	0.007

Table 3. Results of the three models.

Variable	MLR		GWR		MGWR
	Coefficient	VIF	Coefficient (Mean value)	Bandwidth	Coefficient (Mean value)	Bandwidth
Accident types
Collision	0.029	4.20	0.027	792	0.043	1246
Grounding	−0.023	1.29	−0.033	792	−0.023	1246
Striking rocks	0.043	1.33	0.023	792	0.033	1246
Sinking/capsizing	0.280**	1.23	0.297	792	0.274	50
Fire/explosion	0.055*	1.33	0.048	792	0.041	1196
Ship information
Two dry cargo ship involved	0.044	3.46	0.033	792	0.013	1246
One dry cargo ship involved	0.010	2.05	0.017	792	0.008	1246
Fishing ship	0.071*	2.15	0.058	792	0.039	1246
Liquid cargo ship	0.072**	1.34	0.063	792	0.039	508
Gross tonnage	0.261**	1.05	0.293	792	0.234	106
Navigational status	0.093**	1.11	0.102	792	0.073	1246
Environmental characteristics
Time of the day	0.047*	1.02	0.062	792	0.057	831
Good visibility	0.037	1.11	0.044	792	0.057	115
Restricted visibility	−0.024	1.05	−0.030	792	−0.012	1246
Strong wind/wave	0.124**	1.14	0.123	792	0.068	823
Accident cause factors
Judgment error	−0.023	1.08	−0.015	792	−0.001	1246
Lookout failure	0.037	1.35	0.049	792	0.049	989
Operation error Machinery	−0.005	1.37	0.010	792	0.002	1246
Failure	−0.058**	1.32	−0.052	792	−0.036	1246
Intercept	0.000	–	0.000	792	−0.015	164
Observation	1248		1248		1248

*0.05 ≤ p ≤ 0.1, **p ≤ 0.05.

Table 4. Summary statistics for MGWR parameter estimates.

Variable	Mean	STD	Min	Median	Max
Accident types
Collision	0.043	0.004	0.037	0.042	0.057
Grounding	−0.023	0.004	−0.036	−0.022	−0.016
Striking rocks	0.033	0.005	0.026	0.031	0.045
Sinking/capsizing	0.274	0.296	−0.550	0.197	2.361
Fire/explosion	0.041	0.015	0.012	0.049	0.061
Ship information
Two dry cargo ship involved	0.013	0.001	0.010	0.013	0.020
One dry cargo ship involved	0.008	0.003	0.002	0.006	0.016
Fishing ship	0.039	0.004	0.034	0.037	0.061
Liquid cargo ship	0.039	0.054	−0.071	0.039	0.124
Gross tonnage	0.234	0.218	−0.123	0.175	2.199
Navigational status	0.073	0.004	0.066	0.075	0.081
Environmental characteristics
Time of the day	0.057	0.023	−0.008	0.067	0.095
Good Visibility	0.057	0.260	−0.183	−0.024	1.376
Restricted Visibility	−0.012	0.002	−0.018	−0.012	−0.008
Strong wind/wave	0.076	0.016	0.055	0.068	0.139
Accident cause factors
Judgment error	−0.001	0.005	−0.018	0.002	0.003
Lookout failure	0.049	0.017	0.023	0.063	0.069
Operation error	0.002	0.005	−0.007	0.005	0.008
Machinery failure	−0.036	0.002	−0.040	−0.037	−0.032
Intercept	−0.015	0.150	−0.236	−0.064	0.481

Figure 4. Coefficient distributions of influencing factors estimated by MGWR.

Figure 5. (Continued).

Figure 6. (Continued).

Figure 5. Spatial heterogeneity in the effects of micro-scale factors on maritime accidents.

Figure 6. Spatial heterogeneity in the effects of global-scale factors on maritime accident consequence.

Figure A1. Heat maps for the maritime accident variables based on KDE.

Figure A1. (Continued).

Figure A1. (Continued).

Figure A2. Boxplot for marginal effects of MGWR results (outliers are excluded).

Table A1. Nomenclature.

Abbreviation	Full name
AICc	Akaike information criterion
AIS	Automatic Identification System
CCTV	Closed-Circuit Television
FSA	Fujian Maritime Safety Administration
GWR	Geographically Weighted Regression
KDE	Kernel Density Estimation
MGWR	Multi-scale Geographically Weighted Regression
MLR	Multiple Linear Regression
RSS	Residual Sum of Squares
SGWR	Semi-parametric Geographically Weighted Regression
SOC	Score of Change
VIF	Variance Inflation Factor
Symbol	Meaning
I	Moran’s I index
N	Number of observations
x	Variable of interest
$\bar{x}$	Average value of the variable
wpq	Matrix of spatial weights for location p and q
yi	Consequence of maritime accident i
xij	j^th explanatory variable of accident i
${\beta }_j$	Coefficient of the j^th explanatory variable
${\beta }_0$	Intercept term
${\epsilon }_i$	Random error term
(ui, vi)	Location of the accident i
wi (ui, vi)	Spatial weight at location (ui, vi)
$\hat{\beta }\left(u_i,v_i\right)$	location-specific coefficient
dpq	Distance between p and q
b	Critical distance from location p to its M^th nearest neighbor
M	Optimal number of nearest neighbors (bandwidth)
$\hat{\sigma }$	Estimated standard deviation of the error term
tr(S)	Trace of the hat matrix S
${\beta }_{\mathit{bwj}}$	Coefficient of the j^th factor with optimal bandwidth