In recent years the Transport and Road Research Laboratory has carried out a series of major studies of junction safety. In each of these studies, data were collected on the numbers of accidents which had occurred at each site in, typically, the previous four years. Data were also collected on the traffic flows and the geometric and control characteristics of each site. Predictive relationships have been established, in each of these studies, between the accident frequency and the flow, geometric and control variables. The relationships were developed in the form of generalized linear models, and built and tested using the GLIM program as described in: Payne,CD(ed) "The GLIM system release 3.77 manual" published in 1985 by Numerical Algorithms Group, Oxford. The statistical methodology of generalized linear models is an extension of that for multiple linear regression. One of the assumptions is therefore that all the values of the explanatory variables are known without error. Contravention of this assumption can lead to appreciable bias in the model parameter estimates. In previous junction safety studies, this assumption was felt to be safe, since the flow estimates (the only explanatory variables about which there might be any serious concern in this respect) were obtained through long-term counts. However, in future TRRL studies, it is planned to use only short-term counts so that the flow estimates may no longer be safely assumed to be free from random error. The use of the standard GLIM model fitting process could not be relied on to give unbiased results. Because of this, it was felt necessary to develop a model fitting procedure which took proper account, not only of the uncertainty in the accident frequency, but also of the uncertainty in the flow estimates. This was achieved in the form of GLIM macros, thus giving complete compatibility with the model fitting process used in all previous studies. This report describes the development of the statistical methodology, the fitting algorithm and its achievement in the form of GLIM macros, the validation of the approach through simulation tests, and its use for predictive purposes.

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