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\subsubsection{Built Environment Factors}
Table~\ref{tab:be_fac} lists the built environment factors under study. These are descriptive observations of network topology and land use---zoning and road classification. Private roads and commercial land use are rather
under-represented under-represented, as these produce very low traffic volumes. Mixed
land use land-use is used in situations where multiple types of
land use land-use occur near a roundabout. This is typically the case
of where commercial rows
intersecting intersect a residential
neighbourhood which is rarely neighbourhood. The effect may not be comparable to
one or the
other. sum of its parts, however, so is treated separately.
\begin{table}
\caption{Built Environment Factors: Network Class & Land Use}
...
\subsection{Traffic Data}
Traffic flow Traffic-flow data is obtained from the automated analysis video data: vehicle trajectories extracted from video data using computer vision techniques built for traffic analysis applications. In this case, the computer vision tool used is the Traffic-Intelligence project, an open-source traffic-analysis software \cite{Jackson_2013}. See section \ref{data-size} for more details on the source and size of the data.
Trajectory data is
formed obtained from the tracking of moving features within camera space. These feature tracks are a series of continuously measured positions mapped to real coordinates using a scene projection transformation by way of a homography matrix. These features are continuous, forming a path (trajectory) moving through space and time representing
the a road user's movement through the scene. Features are grouped together into objects using specifically calibrated algorithms for the task of identifying individual road users in the a scene (though context-insensitive classification is still a work in progress). Some secondary filtering techniques were developed to automate validation and error correction \cite{Jackson_2013, St_Aubin_2014}.
Traffic flow and flow ratios can be obtained by performing counts on these objects according to the context of the specific metric. In this case we collect per-lane per-hour counts over the time of the study. Flow ratio is calculated as follows:
\begin{equation} \label{eqn:flow_ratio} Q_r = Q_{approach}/(Q_{roundabout} + Q_{approach}) \end{equation}
where $Q_{roundabout}$ is the count of vehicles entering the weaving zone from within the roundabout and $Q_{approach}$ is the count of vehicles entering the weaving zone from the approach. A low $Q_r < 0.33$ indicates a large traffic flow arriving from a different section of the roundabout (users who have priority) with little mixing. A high $Q_r > 0.66$ indicates a large traffic flow arriving from the approach (users who do not have priority) with little mixing. A $Q_r$ between 0.33 and 0.66 indicates an even balance of traffic flow between the approach and inside the roundabout with good mixing. This is more common with low
flows flows, as priority rules tip the balance of flow in favour of those already in the roundabout at flow saturation. A
polarised polarized flow ratio is a flow ratio less than 0.33 or greater than 0.66.
\subsubsection{Speed}
...
\subsubsection{Time-to-collision}
A
discretised discretized motion pattern matrix method developed specifically for roundabouts \cite{St_Aubin_2014} is used for this study. We also elect to model all traffic events, using a conservative minimum probability of collision detection of 0.001, and using the indicator aggregation by the 15th percentile unique per user pair as
is described in \cite{St_Aubin_2015}.
\subsection{Site Selection}
Site selection was performed according to a number of criteria including practical constraints and statistical representation. Data collection feasibility was scored on a five-point scale measuring data collection cost and quality and sorted to generate a feasibility rank. Among a population of nearly one hundred candidate roundabouts in the province of Québec, starting from the most feasible, thirty sites were chosen to provide a good representation of design and
land use land-use characteristics, knowing that a fraction of these sites would have to be rejected due to logistical issues (e.g. adverse weather, road closures, or equipment failure hampering data collection efforts). In particular:
\begin{itemize}
\item An adequate geographical coverage of the province of Québec and
land use land-use types was desired. Sites were selected throughout all but one of the the major populated regions of Québec, as well as some of the more rural areas to provide regional representation. As listed in Table~\ref{tab:be_fac}, representation of the built environment factors is
adequate though adequate, although with a few exceptions. Notably, roundabouts on private roads are difficult to access for data collection and, in any case,
provides provide little safety information as traffic flows are too small. Also, while roundabouts can often be found in school or commercial zones, these roundabouts did not serve through-traffic, serving instead as limited access points for parking lots or campus roads. These sites were rejected.
\item Roundabouts located on the territory of the provincial transportation agency are all built to very similar specifications and are significantly more consistent in design than municipal roundabouts. However, provincial roundabouts tend to serve more network classes than municipal
roundabouts roundabouts, which serve collector roads for the most part.
40~\% Forty percent of the sites were located on provincial
territory territory, while the remainder were strewn across seven different municipalities.
\end{itemize}
\subsection{Modelling}
Speed can be nicely averaged as it is generally normally distributed.
However, TTC
however is not always so nicely
distributed: distributed. Therefore different aggregation methods should
therefore be used.
Instead So instead of using aggregation, this data will be analysed in a disaggregated manner. The data is thus effectively unbalanced panel data, where sites are the panels containing individual observations of behaviour (speed, TTC indicators, gap acceptance). Random effects modelling is chosen for the analysis using the formula
\begin{equation} \label{eqn:rextreg_model} ln(Y_{ij}) = \mu + {\sum}^{n}_{k=1} \beta_k X_{kij} + u_{ij} + \epsilon_{ij} \end{equation}
where $Y_{ij}$ is the safety indicator of the $j$th road user at the $i$th site, $\beta_k$ is the coefficient of factor $X_{kij}$ from $k=1..n$ factors and $\mu$ is the average safety indicator (base case). $u_{ij}$ and $\epsilon_{ij}$ are the between-entity error and within-entity error respectively. Regressing for the natural logarithm instead of the dependant variable directly mitigates issues with non-normal distributions, which is particularly the case with TTC.
has the effect A useful model for evaluating the effects of sites has a large between-$R^2$ and minimises within-$R^2$ effects.
