deletions | additions       diff --git a/subsection_Regression_Results_subsubsection_Speed__.tex b/subsection_Regression_Results_subsubsection_Speed__.tex  index 203e518..44cdeaa 100644  --- a/subsection_Regression_Results_subsubsection_Speed__.tex  +++ b/subsection_Regression_Results_subsubsection_Speed__.tex 
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\subsubsection{Speed}  A stepwise linear regression is performed on mean road user merging zone  speed measured (in km/h) at each merging zone individually, testing all explainable differences between sites, shown in Table~\ref{tab:analysis_zones}. The coefficients of regression, adjusted $R^2$, Wald test score, and number of observations are provided in Table~\ref{tab:se_regression}. Table~\ref{tab:se_regression_mean_speed}.  Note that roundabout outside radius, flow ratio, land use, urban density, and construction year are were  notfound to be  significant in predicting mean speed. Instead, a good model (with an adjusted $R^2 = 0.658$) with only two factors remains: \begin{itemize}  \item A significant reduction in mean speed of 4.5~km/h is observed at the Swedish sites.  \item Increases in hourly traffic volume are correlated with reductions in mean speed as well. This is not surprising, given standard traffic flow theory (e.g.\ Greenshield's Model).  \end{itemize}  These conclusions are similar to those drawn from the exploratory analysis. More importantly, however, is the confirmation that none of the factors controlled between sites are shown to have an impact on speed, analysis,  suggesting that regional, cultural, and road user education regional  effects such as education, enforcement, or culture  might be in play instead. %stepwise, pr(.1001) pe(.1): regress mean_speed sweden hourlyflowvehhln outsideRadius_m yearsSinceBuilt flowRatio lu2 d2 d3  %stepwise, pr(.1001) pe(.1): regress start_gap_lt5s_median sweden hourlyflowvehhln outsideRadius_m yearsSinceBuilt flowRatio lu2 d2 d3  \begin{table}[ht]  \caption{Linear Regression Models for Mean Speed and Median Lag Yielding Post-Encroachment Time}  \centering  \label{tab:se_regression} \label{tab:se_regression_mean_speed}  \begin{tabular}{p{1.5in}|p{0.75in}p{0.5in}|p{0.75in}p{0.5in}}  \hline   & \multicolumn{2}{p{1.25in}}{Mean Speed} & \multicolumn{2}{p{1.25in}}{Median Lag YPET}\\ \gls{YPET}}\\  & Coefficient & P>|t| & Coefficient & P>|t| \\  \hline   _cons & 35.898 & 0.000 & 1.303 & 0.018 \\ 
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\subsubsection{Yielding Post-Encroachment Time}  Another A  stepwise linear regression is performed on median lead and lag yPET below 5~s at each site, to test all explainable differences between sites, shown in Table~\ref{tab:analysis_zones}. The Table~\ref{tab:analysis_zones}.The  coefficients of regression, adjusted $R^2$, Wald test score, and number of observations are provided in Table~\ref{tab:se_regression}. Table~\ref{tab:se_regression_mean_speed}.  Region is not found to be significantly correlated with median lead and lag yPET, although the Outside Radius and Flow variables are found to be associated with lag yPET, having a moderately powerful relationship.This would suggest that a larger rounabout radius moderatly increases lag yPET (a larger roundabout means there is more space for road users to interact) while a greater flow of traffic decreases it (unsurprisingly, as gap distances shrink with increasing traffic).  \subsubsection{Time-to-Collision}  A stepwise linear regression of motion pattern-based  serious $TTC_{15^{th}cmp}$ TTC  events (measured in events per hour) is performed, using weighted SEC methodology with a threshold of $\zeta = 1.5$ seconds. No statistically significant model is found, however. Next, a That leaves  SCC-based regression is conducted. As mentioned earlier, $TTC_{15^{th}cmp}$ values in this analysis are disagregated at as  the site level, forming panel data. As such, a final analysis to be conducted. A  random effects regression model  is used, using the log ofeach  the dependent observation of $TTC_{15^{th}cmp}$: variable TTC:  \begin{equation}  ln(TTC_{15_{ij}}) = \alpha + {\sum}_{k} \beta_k X_{kij} + u_{ij} + \epsilon_{ij}  \label{eq:se_ttc_regress_random_effects}  \end{equation}  using identical notation as in equation~\ref{eq:cg_ttc_regress_random_effects}.  A SCC random effects regression of motion pattern-based \nth{15} centile TTC (measured in seconds) is performed between the Québec and Swedish sites. Results are shown in Table~\ref{tab:se_regression_ttc_continuum}. This yields a moderately predictive model with a between $R^2 = 0.425$ (accounting for differences between merging zone). This is accounted for by the Swedish variable, as it is associated with increasing TTC by 0.293~s on average, thus leading to hypothetical reductions in collision probability. A minor within-effect is also noted, with fifteen-second traffic exposure associated with an increasing TTC. As evidenced with the angle of incidence parameter, user pair with a small angle of incidence, i.e.\ rear end conflict, are associated with lower TTC values than with a larger angle of incidence, i.e. side swipe conflict. The sign and magnitude of the coefficient associated with this parameter is consistent with the coefficient for angle of incidence observed in Chapter~\ref{ch:C3}. Finally, it is worth noting that the approach dominance and absolute flow ratio parameters are not significantly correlated with TTC as is the case with the Québec roundabout merging zone exclusively. Furthermore, construction year (or elapsed time since roundabout construction) is not correlated significantly either. \begin{table}[ht]  \caption{Random Effects Regression Models for Motion Pattern-Based \nth{15} Centile Time-to-Collision (SCC)}  \centering  \label{tab:se_regression_ttc_continuum}  \begin{tabular}{p{3.0in}|p{1in}p{1in}} \begin{tabular}{p{2.0in}|p{0.75in}p{0.5in}}  \hline  & Coefficient & P>|t| \\ \hline _cons & 0.583 & 0.000 \\ Swedish Site & 0.293 & 0.029 \\ \hline Fifteen Second Exposure & 0.01690 & 0.000 \\ Interaction Angle & 0.003279 & 0.000 \\ \hline \textbf{Within $R^2$} & \multicolumn{2}{|c|}{0.0540} \multicolumn{2}{p{1.25in}}{0.0540}  \\ \textbf{Between $R^2$} & \multicolumn{2}{|c|}{0.4244} \multicolumn{2}{p{1.25in}}{0.4244}  \\ \textbf{Overall $R^2$} & \multicolumn{2}{|c|}{0.0204} \multicolumn{2}{p{1.25in}}{0.0204}  \\ \textbf{Wald prob > F} & \multicolumn{2}{|c|}{0.0000} \multicolumn{2}{p{1.25in}}{0.0000}  \\ \textbf{Observations} & \multicolumn{2}{|c|}{23565} \multicolumn{2}{p{1.25in}}{23565}  \\ \textbf{Groups} & \multicolumn{2}{|c|}{19} \multicolumn{2}{p{1.25in}}{19}  \\ \hline  \end{tabular}  \end{table}