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Two Problems of Averaging Arising in the Estimation of the Relationship Between Accidents and Traffic Flow

A function linking the expected accident frequency to traffic flow is called a safety performance function (SPF). SPFs are estimated from data for various facilities and accident types. Typically, accident counts over a period of a year or more, and estimates of average flow for such periods, serve as data. The ideal is for SPFs to represent cause-effect regularities. However, because accident counts are for a long time period and because average flows are used, two issues of averaging arise. First, the cause-effect relationship is between accidents and the flows prevailing near the time of accident occurrence. Therefore, ideally, these should be the argument of the SPF. In practice, however, either because of lack of detail or difficulties of estimation, average flows are used for estimation. The question is what problems arise when average flows, such as annual average daily traffic, instead of the flows at the time of the accident are used as the argument of the SPF. This is the argument averaging problem. Second, there are at least two (daytime and nighttime) and perhaps many more cause-effect SPFs that prevail in the course of a year. Ideally, each relationship should be estimated separately. The question is what problems arise if one joint SPF is estimated when two or more separate functions should have been used. This is the function averaging problem. After analysis, how to account and how to correct for the argument averaging problem are shown. At this time, avoiding the function averaging problem by estimating daytime and nighttime SPFs separately can be the only recommendation.