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\subsection{Behaviour and Safety Indicators}  v  The parameters of interest for this particular study are the most notable surrogate measures of safety: two measures obtained directly from the observed road user trajectories, speed and post-encroachment time (PET)~\citep{allen1978analysis}, and time-to-collision (TTC)~\citep{Hayward_1971}, a measure derived from position and speed based on assumptions of the road users' expected motion.   Speed is widely regarded in the literature as a useful predictor of collision severity given the relationship between speed and kinetic energy carried by a road user in motion~\citep{Fildes_1993, elvik2004speed}.  
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While surrogate safety measures such as speed are easily summarised over time at the site level using descriptive statistics (given the consistency of normal-like unimodal distributions of speed observations at the sites), TTC is less well summarised as it tends to have a distribution shape that varies from one site to the next. There are generally two approaches used in the literature to making TTC comparisons between sites:  \begin{itemize}  \item serious event comparison (SEC), which sets an assumed target threshold or set of rules of ``seriousness'', e.g.\ 1.5~s corresponding to the commonly cited driver reaction times of 1.5~s~\citep[][]{Hyden_1987, Green_2000}, and counts the number of events (pairs of road users) where the representative safety indicator, e.g.\ $TTC_{15^{th}cmp}$, meets this criterion. This approach thus evaluates the rate of serious events per unit of traffic exposure, or converts them into predicted accidents using conversion factors~\citep{Hyden_1987}. This approach is simple to implement and is the most analogous to current approaches to road safety study, but has the two main disadvantages being that it is a very coarse measure, and it makes the most assumptions about the significance of the safety indicator, e.g.\ in this case, a strong relationship between $TTC_{15^{th}cmp}$ and a reaction time of 1.5~s is assumed. If probabilistic motion prediction methods are used, as in the case of discretised motion patterns, the number of serious events can be further weighed by their collision probability, resulting in a weighted SEC \cite{St_Aubin_2016_thesis}.  \item safety continuum comparison (SCC), which attempts instead to evaluate the effects of each safety indicator individually without explicitly attributing collision probability or ``seriousness'' to safety indicators, and thus without investigating equivalent accidents or events. This approach is disaggregated by nature: all safety indicators impact safety in proportion to their value. This results in a hierarchical data set: each site having multiple road user interactions, each having different $TTC_{15^{th}cmp}$. $TTC_{15^{th}cmp$.  \end{itemize}  %removed: I don't understand Stated differently, the objective of this approach is to decrease TTC overall