deletions | additions       diff --git a/Results TTC.tex b/Results TTC.tex  index 576edd5..07bea96 100644  --- a/Results TTC.tex  +++ b/Results TTC.tex 
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Table~\ref{tab:simple_speed_regression} lists the coefficients and p-values for three factors which stand out: commercial and institutional land-uses as well as number of exit lanes off the roundabout are found to have a traffic calming effect on an average speed of 42 km/h for vehicles travelling through the weaving zone by 5 to 10 km/h. Number of exit lanes having a negative effect on speed is unexpected, may be explained by more regular arrivals of inside of the roundabout providing fewer opportunities for vehicles on the approach to enter the roundabout without stopping. Regardless, in a future study, it should be interesting to compare this effect with yielding behaviour and gap times. Unsurprisingly, speed limits are also correlated with speed, though they are covariant with many built environment factors, so are ignored. The R-squared for this first model is 0.2766, which offers modest explanatory power. To improve results, site clustering and random effects regression is performed next.  \begin{table}  \caption{Linear regression for aggregated mean speed} speed (p-values and significance in parenthesis}  \label{tab:simple_speed_regression}  \begin{tabular}{llrrr} \begin{tabular}{lrrr}  \hline  \textbf{Factor} & \textbf{Variable name} \textbf{Coefficients}  & \textbf{Coefficients (p-value)} \textbf{Coefficients}  & \textbf{Coefficients (p-value)} & \textbf{Coefficients (p-value)} \textbf{Coefficients}  \\ \hline Constant &\_cons &  42.01 (0.000 ***) & 4.74 (0.002 ***) & 26.91 (0.000 ***) \\ Commercial land-use &lu2 &  -5.51 (0.053 *) & ~ & ~ \\ Institutional land-use &lu6 &  -9.41 (0.050 **) & ~ & ~ \\ Number of exit lanes &n\_exit\_lanes &  -6.80 (0.041 **) & ~ & ~ \\ Approach speed limit &app\_speed\_limit &  ~ & 0.32 (0.001 ***) & ~ \\ Apron width &w\_apron &  ~ & -1.51 (0.056 *) & ~ \\ Inflow per hour per lane &inflow\_ph\_pl &  ~ & ~ & 0.02 (0.081 *) \\ \hline \textbf{R-squared} &~ &  0.277 & 0.2446 & 0.0760 \\ \textbf{No. observations} &~ &  41 & 41 & 41 \\ \hline  \end{tabular}  \end{table} 
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\subsection{Disaggregated Speed Regression}  To better manage results due to the number of variables, k-means clustering is employed on all of the variables. Several clusters were performed using between three and six centroids to find a suitable model that i) produces the most meaningful and interpretable clusters, ii) produces a random effects regression model with explanatory power, and iii) where p-values still remain relatively significant. However, because we know the different indicators are statistically independent for the most part, we find that different clusters offer different explanatory power for each dependant variable. Table~\ref{tab:cluster_speed_profile} lists the distribution of observations (at the site level and at the disaggregated level) for the clusters used to model speed and offers a short profile for each. %  A selection of variable statistics are presented in Table~\ref{tab:cluster_speed_stats}. \begin{table}  \caption{K-means cluster profile for speed regression} 
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\end{tabular}  \end{table}  \begin{table} %\begin{table}  %  \caption{K-means cluster select statistics for speed regression} %  \label{tab:cluster_speed_stats} %  \begin{tabular}{l|lllllll|ll} %  & & & & {(min mean max)} & \multicolumn{1}{c}{} & & & (mode) & \\ %  & \textbf{n\_start\_lanes} & \textbf{n\_app\_lanes} & \textbf{n\_exit\_lanes} & \textbf{a\_quad\_size} & \textbf{r\_out\_start} & \textbf{d\_app\_inter} & \textbf{flowratio} & \textbf{land\_use} & \textbf{network\_class} \\ \hline c1\_s %c1\_s  & 1 & 1 & 1 & 90.0 & 17.5 & 438 & 0.17 & & \\ %  & 1 & 1.5 & 1 & 97.3 & 23.0 & 1197 & 0.25 & Residential & Arterial \\ %  & 1 & 2 & 1 & 105.0 & 27.0 & 2924 & 0.38 & & \\ \hline c2\_s %c2\_s  & 1 & 1 & 1 & 75.0 & 22.5 & 36 & 0.12 & & \\ %  & 1 & 1 & 1 & 92.5 & 24.4 & 233 & 0.45 & Industrial & Regional Highway \\ %  & 1 & 1 & 1 & 105.0 & 26.0 & 443 & 0.75 & & \\ \hline c3\_s %c3\_s  & 1 & 0 & 1 & 45.0 & 17.5 & 67 & 0.12 & & \\ %  & 1.15 & 1.15 & 1 & 91.9 & 22.9 & 330 & 0.69 & Residential & Highway Ramps \& Arterials \\ %  & 2 & 2 & 1 & 145.0 & 27.5 & 583 & 0.98 & & \\ \hline c4\_s %c4\_s  & 1 & 1 & 1 & 90.0 & 13.5 & 45 & 0.00 & & \\ %  & 1 & 1 & 1.17 & 96.7 & 16.8 & 218 & 0.51 & Residential & Collector \\ %  & 1 & 1 & 2 & 130.0 & 18.5 & 818 & 0.98 & & \\ \hline c5\_s %c5\_s  & 2 & 1 & 1 & 45.0 & 43.5 & 62 & 0.16 & & \\ %  & 2 & 1.75 & 1.5 & 65.0 & 48.4 & 107 & 0.60 & Mixed & Arterial \\ %  & 2 & 2 & 2 & 90.0 & 54.0 & 200 & 0.92 & & \\ \hline c6\_s %c6\_s  & 2 & 1 & 2 & 90.0 & 20.0 & 55 & 0.33 & & \\ %  & 2 & 1.83 & 2 & 93.3 & 24.2 & 173 & 0.84 & Commercial & Arterial \\ %  & 2 & 2 & 2 & 110.0 & 31.5 & 342 & 0.98 & & \\ \hline %  \end{tabular} \end{table} %\end{table}  This regression model offers relatively good explanatory power. The coefficients and statistical test results are provided in Table~\ref{tab:re_speed_regression} All but cluster c6\_s (2-lane arterials) provides moderate to very strong statistical significance. Cluster c1\_s (single-lane residential arterial) is associated with the lowest speeds. From the cluster characteristics, we gather that high and moderate flow ratios have an important effect of increasing speed. Unsurprisingly, the highest speeds attributed to regional highway roundabouts. Large-diameter, 2-lane, roundabout-converted traffic circles had the poorest speed results, probably because the approach angle remained tangential to the circle instead of the usual mostly orthogonal approach of smaller roundabouts. Interestingly, roundabouts situated in residential neighbourhoods on collector streets (cluster c4\_s) were associated with higher speeds than highway ramps (cluster c3\_s), despite the smaller size. This may be attributed to significantly lower flows and thus fewer conflicts. 
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\label{disagregated_ttc_reg}  Table~\ref{tab:cluster_ttc_profile} lists the distribution of observations (at the site level and at the disaggregated level) for the clusters used to model TTC and provides a short profile for each. Weaving zones are slightly less well balanced across groupings, though individual observations are better distributed. Also of note is that clusters c5\_s and c5\_t are identical. %  Variable statistics are presented in Table~\ref{tab:cluster_ttc_stats}. \begin{table}  \caption{K-means cluster profile for TTC regression} 
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\end{table}  \begin{table}[h] %\begin{table}[h]  %  \caption{K-means cluster select statistics for ttc regression} %  \label{tab:cluster_ttc_stats} %  \begin{tabular}{l|lllllll|ll} %  & & & & {(min mean max)} & \multicolumn{1}{c}{} & & & (mode) & \\ %  & \textbf{n\_start\_lanes} & \textbf{n\_app\_lanes} & \textbf{n\_exit\_lanes} & \textbf{a\_quad\_size} & \textbf{r\_out\_start} & \textbf{d\_app\_inter} & \textbf{flowratio} & \textbf{land\_use} & \textbf{network\_class} \\ \hline c1\_s %c1\_s  & 1 & 1 & 1 & 60.0 & 13.5 & 45 & 0.00 & & \\ %  & 1.27 & 1.18 & 1.18 & 93.8 & 18.7 & 223 & 0.48 & Residential & Collector \\ %  & 2 & 2 & 2 & 130.0 & 22.0 & 818 & 0.98 & & \\ \hline c2\_s %c2\_s  & 1 & 0 & 1 & 45.0 & 17.5 & 36 & 0.12 & & \\ %  & 1 & 1 & 1 & 87.9 & 23.4 & 565 & 0.58 & Industrial & Regional Highway \\ %  & 1 & 2 & 1 & 105.0 & 27.5 & 2924 & 0.98 & & \\ \hline c3\_s %c3\_s  & 2 & 2 & 2 & 90.0 & 21.0 & 55 & 0.83 & & \\ %  & 2 & 2 & 2 & 94.0 & 25.0 & 194 & 0.94 & Industrial & Arterial \\ %  & 2 & 2 & 2 & 110.0 & 31.5 & 342 & 0.98 & & \\ \hline c4\_s %c4\_s  & 1 & 2 & 1 & 90.0 & 17.5 & 580 & 0.17 & & \\ %  & 1 & 2 & 1 & 94.7 & 23.8 & 671 & 0.21 & Residential & Arterial \\ %  & 1 & 2 & 1 & 97.0 & 27.0 & 717 & 0.23 & & \\ \hline c5\_s %c5\_s  & 2 & 1 & 1 & 45.0 & 43.5 & 62 & 0.16 & & \\ %  & 2 & 1.75 & 1.5 & 65.0 & 48.4 & 107 & 0.60 & Mixed & Arterial \\ %  & 2 & 2 & 2 & 90.0 & 54.0 & 200 & 0.92 & & \\ \hline c6\_s %c6\_s  & 1 & 1 & 1 & 137.0 & 25.0 & 151 & 0.59 & & \\ %  & 1 & 1 & 1 & 141.0 & 25.0 & 367 & 0.66 & None & Highway Access Ramp \\ %  & 1 & 1 & 1 & 145.0 & 25.0 & 583 & 0.73 & & \\ \hline %  \end{tabular} \end{table} %\end{table}  This regression model offers moderately good explanatory power. The coefficients and statistical test results are provided in Table~\ref{tab:re_TTC_regression}. Clusters c5\_s and c6\_s are not statistically significant. Small, residential, local roundabouts are associated with the second-worst (lowest) TTC performance, after traffic circle conversions which were noted for their issues with higher speed. The best performing group, in terms of safety appears to be 2-lane arterials with excessively high flow ratios (c3\_s). This is probably explained due to the extremely low amount of interactions generated at the weaving zone---instead these results are probably governed by TTC measures generated from lane changing manoeuvres. Clusters c4\_t (Hybrid lane arrangement arterials with very low flow ratios) and cluster c2\_t (single-lane regional highways and arterials with speed limits and polarised flow ratios) offer the next best TTC performance. The most striking aspect in this model is that higher TTC appears to be associated with flow ratio extremes where as lower TTCs (more dangerous) appear to be associated with highly mixed flow ratios. This might be explained by the increase in the generation of complex merging manoeuvres when flows are equivalent on both the roundabout and it's approach. 
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\subsection{TTC Distributions by Cluster}  Using the comparison methodology described in \cite{St_Aubin_2015}, Figure~\ref{fig:cdf_mot_pat_15th_P0001} provides the cumulative distribution functions of TTC for the clusters c1\_t through c6\_t. The unambiguous left-shift of TTC observations for cluster c3\_t and right-shift for cluster c5\_t are consistent with the results of the TTC regression model presented in \ref{disagregated_ttc_reg}: c3\_s is associated with the greatest benefits in safety. Clusters c1\_s, c2\_s, c4\_s, and c6\_s are inconclusive using this approach.