事故頻次與嚴重度之時空相依性：多項廣義卜瓦松模式

Abstract

為了將多期肇事資料中的肇事頻次、肇事嚴重程度時空相依等關聯性同時予以考量，本研究發展了數種以多項廣義卜瓦松(下稱MGP)為基礎之事故分析模式。基此，本研究首先建立基礎MGP模式與考慮誤差分量之多項廣義卜瓦松模式(下稱EMGP)探討肇事頻次與肇事嚴重程度之整合。本研究係以2005年臺灣國道1號事故資料為例，驗證前述所提模式。實證結果顯示EMGP模式有相對較佳之解釋能力，因其連接不同嚴重程度肇事間之間的相關性，從而更精確估計不同嚴重性類型的事故頻次。實證結果也顯示風險因素對肇事頻次與嚴重性之影響效果不一致，交通相關因素對肇事頻次與嚴重性要幾何相關因素影響大。 為於上述模式納入空間相關性，本研究建立空間自相關EMGP模式(下稱Spatial error-EMGP)與空間相依函數EMGP模式(下稱Spatial exogenous-EMGP)兩模型，並於前述高速公路實證例進行驗證與比較。Spatial error-EMGP模式指定空間自相關(spatial auto-regression)與空間移動平均誤差(spatial moving average)等空間誤差結構用以模化空間相依性。Spatial exogenous-EMGP將空間相依之效果透過外生之空間函數模化，函數內則納入總括交通與幾何等相關條件的兩變數，因此該空間函數能用以解釋空間相依性。估計結果顯示Spatial error-EMGP統計績效要Spatial exogenous-EMGP好，且能解釋空間相依性成因。Spatial exogenous-EMGP估計結果也顯示道路幾何因素影響空間相依性之影響範圍，交通因素與空間相依性之影響程度有關。 最後，為進一考量多期資料的時間相依性，本研究建立考慮誤差分量與時空相之多項廣義卜瓦松模式(下稱ST-EMGP)，其係推廣Spatial exogenous-EMGP模式之空間相依函數，增加空間尺度因子(spatial size coefficient)與序列相關係數(temporal serial coefficient)以反映時空相依程度。本研究以前述高速公路2004-2008年資料進行驗證。估計結果顯示ST-EMGP模式相較前述模式要有更加統計績效，其估計結果也指出時空相依性同時存在並交互影響，若忽略時間相依性會高估空間相依性之影響幅度，低估空間相依性之影響範圍。透過分析時空相依性效果可知，時間相依性受交通因素影響且與事故頻次有所關聯，幾何因素主要與空間相依性有關，且對事故嚴重性影響相對高。本研究發展之ST-EMGP模式可釐清時空相依性，與其對肇事頻次與嚴重性之關聯影響。另依據該模式評估結果可研提相應之安全改善策略。

To simultaneously account for the correlations among crash frequency, crash severity and spatiotemporal effect on panel crash data, the study develops various multinomial generalized Poisson (MGP) models to simultaneously accommodate above dependencies. At first, the study established the basic multinomial generalized Poisson (MGP) model and MGP with error components (EMGP) to simultaneously modeling crash frequency and severity. Additionally, the case for Taiwan No. 1 Freeway accidents at year 2005 is used to validate the above mentioned models. The empirical results show that the EMGP model demonstrated relatively superior on goodness-of-fit, since it captured the correlations among different levels of crash, so as to more precisely estimate crash frequency of different crash severity type. The estimation results also showed that risk factors contributing to crash frequency and severity differ markedly. Traffic related factors have larger effects on crash severity and frequency than geometric factors in the freeway case. For accommodating spatial dependence on the above established EMGP model, two spatial EMGP models, spatial error-EMGP and spatial exogenous-EMGP, are proposed and validated in the same freeway case. The spatial error-EMGP model incorporates spatial error in the structure of spatial auto-regression and spatial moving average to capture spatial correlation effects; while the spatial exogenous-EMGP model introduces the spatial exogenous functions composed of two state parameterized functions associated with traffic and geometric composite variables to explain the sources of spatial dependence. The results show that the spatial exogenous-EMGP model have better statistical performance than spatial error-EMGP, and explained the source of spatial dependence. The spatial exogenous-EMGP estimation also shows the road geometric factors can significantly influence the spatial impact range of spatial dependence, and traffic factors are associated with spatial correlation magnitudes. Lastly, to further consider the temporal dependence in multi-period crash data, an extension of the spatial exogenous-EMGP is developed to simultaneously accommodate both spatial and temporal dependencies by using spatial size and temporal serial coefficients to represent the degree of spatiotemporal dependence (namely, the ST-EMGP model). The same case study on five consecutive years (2004–2008) crash data in Taiwan’s No. 1 Freeway is conducted to validate the model. The estimation results show that the ST-EMGP model is better than above-mentioned models in terms of statistical performance. The ST-EMGP estimation also indicates that spatial and temporal dependencies exist and correlate mutually. Spatial dependence may overstate its impact magnitude, but underestimate its impact range when temporal dependence is ignored. Through analyzing spatiotemporal effects, temporal effects, mainly affected by traffic characteristics, are more germane to crash frequency, and spatial effects, mainly affected by geometric configuration, are more germane to severe crash severity levels. The developed ST-EMGP model is able to elucidate the sources of spatiotemporal dependence as well as their effects on crash frequency and severity. Relevant safety improvement strategies are proposed accordingly from the evaluation of ST-EMGP model.