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Highway Winter Crash Modeling with Stochastic Covariates and Missing Data

机译:高速公路冬季碰撞建模与随机协变量和缺失数据

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This paper aims at providing a stochastic approach for modeling highway collision in winter time and also identifying the most probable contributing factors. Logistic regression model is applied to crash data in which the probability of collision depends on the weather process and other predictors. The weather process is modeled as a finite state space, multivariate discrete time Markov chain. The likelihood function of fully observed dataset is expressed in closed form under the assumption that both weather and crash processes are monitored continuously over a specified time interval. Because some covariates for some crash data points are not fully observed, maximizing the log-likelihood function is quite difficult. Thus the closed form of the complete and pseudo likelihood functions for estimating the parameters of the model by Expectation-Maximization (EM) algorithm for partially observed dataset are derived. The likelihood function of fully observed dataset is presented and the parameters have been estimated for North Ontario highway selected segments crash data. The forecasting performance of the introduced stochastic model is compared with non-stochastic forecasting and actual collision data. The mean absolute deviation (MAD) and relative percentage deviation (RPD) are used for the verification of probability forecasts. The result shows that the precision in crash prediction using the proposed model is very good.
机译:本文旨在提供一种在冬季建模的随机碰撞,以及识别最可能的贡献因素。 Logistic回归模型应用于崩溃数据,其中碰撞概率取决于天气过程和其他预测因子。天气过程被建模为有限状态空间,多变量离散时间马尔可夫链。完全观察到数据集的似然函数在假设上以指定的时间间隔连续监测天气和崩溃过程,以封闭式表单表示。由于没有完全观察到一些崩溃数据点的一些协变量,因此最大化日志似然函数非常困难。因此,导出了用于通过期望的数据集的期望最大化(EM)算法来估计模型的完整和伪似然函数的封闭形式。提出了完全观察到数据集的似然函数,估计参数为北安大略省高速公路选择段崩溃数据。将引入的随机模型的预测性能与非随机预测和实际碰撞数据进行了比较。平均绝对偏差(MAD)和相对百分比偏差(RPD)用于验证概率预测。结果表明,使用所提出的模型的碰撞预测精度非常好。

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