The Power and Exponential models, logit form

The Power and exponential models are used here for linking the accident risk to any single variable - speed, occupancy, time headway. We call POWER Ra a Power model where a second explanatory variable - the rain occurrence - is introduced the parameters are estimated on its logit form, where this model reads  

When the risk is not monotonous with the traffic variable, a supplementary term (here parabolic) is introduced. However, due to an insufficient number of accidents, it was not possible to estimate four parameters models are then estimated on datasets excluding rain, where the rain occurrence is replaced by the square of the traffic variable in that case, the name of the model (POWER or EXPO) is indexed by NoRain and by the abbreviation Para for parabolic y is the coefficient of the square of the indicator the direction of variation of the risk depends on whether the traffic variable F, is below/above the value -p/(2.y). 

The main relationships useful for assessing the speed limit reduction are presented in the following. The processing is slightly different from Ait-Belkacem [AIT 12], on the same sets of data. A more complete presentation of the relationships can be found in Aron et al. [ARO 15] they include the impacts, on the accident count, of indicators based on a short time headway and on the relative speed. 

Values of the coefficients of significant relationships (single vehicle accidents, daytime) 

Accidents are often due to the behavior of a single driver (speeding), but this does not systematically appear at an aggregated 6-minute level. Moreover, in some 

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