Spatial autocorrelation is a measure of the correlation of an observation with Vehicular Crashes other observations through space. Most statistical analyses are based on the assumption that the values of observations are independent of one another. Spatial autocorrelation Vehicular Crashes violates this assumption, because observations at near-by locations are related to each other, and hence, the consideration of spatial autocorrelations has been gaining attention in crash data modeling in recent years, and research have shown that ignoring this factor may lead to a biased estimation of the modeling parameters. This paper examines two spatial autocorrelation indices: Moran’s Index; and Getis-Ord Gi* statistic to measure the spatial autocorrelation of vehicle crashes occurred in Boone County roads in the state of Missouri, USA for the years 2013-2015. Since each index can identify different clustering patterns of crashes, therefore this paper introduces a new hybrid method to identify the crash clustering patterns by combining both Moran’s Index and Gi* statistic. Results show that the new method can effectively improve the number, extent, and type of crash clustering along roadways.

In many vehicle crash data, geographic relationships among crashes can exist, and this phenomenon is termed spatial autocorrelation, which is a measure of the correlation of a crash with other crashes through space. Most statistical analyses are based on the assumption that the values of observations in each sample are independent of one another. Spatial autocorrelation violates this assumption, because samples taken from nearby locations are related to each other, and hence, they are statistically not independent of one another [1] [2] . Therefore, the consideration of spatial autocorrelations has been gaining attention in crash data modeling in recent years, and researchers have shown that ignoring this factor may lead to a biased estimation of the model parameters [3] – [12] . Taking the spatial autocorrelation into account in crash modeling can improve model parameter estimation, and the overall model fit [8] [13] . The spatial autocorrelation phenomenon can be best summarized by the Tobler’s first law of Geography that everything is related to everything else but those which are near to each other are more related when compared to those that are further away [14] .

Spatial autocorrelation can be positive or negative among observations. Positive spatial autocorrelation occurs when observations having similar values are closer (i.e. clustered) to one another, and negative spatial autocorrelation occurs when observations having dissimilar values occur near one another [2] [15] . Two problems may be faced when sample data has a locational dimension: 1) the existence of spatial autocorrelation between the observations, and 2) the variation of this relationship over the space that could be described as spatial heterogeneity [16] or spatial non-stationarity [17] . Hence, spatial autocorrelation must be incorporated in modeling crash data to properly account for the effect of spatial correlation and any unobserved spatial heterogeneity that may exist in the crash data. To assess spatial autocorrelation, a distance measure must be specified in order to define what is meant by two observations being close together. These distances are usually presented in the form of a weight matrix, which defines the relationships between locations at which the observations occur [18] . If data are collected at n locations, then the weight matrix will be n × n with zeroes on the diagonal. The weight matrix is often row-standardized, (i.e. all the weights in a row sum to one), and can be constructed given a variety of assumptions [2] , such as, a constant distance that represents the weight for any two different locations; a fixed weight for all observations within a specified distance; or k nearest neighbors.