Regression Results

Speed

A 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}, with the exception of collision statistics, given that this dataset isn’t as reliable. The coefficients of regression, adjusted \(R^2\), Wald test score, and number of observations are provided in Table \ref{tab:se_regression_mean_speed}. Note that roundabout outside radius, flow ratio, land use, urban density, and construction year were not significant in predicting mean speed. Instead, a relatively good model (with an adjusted \(R^2 = 0.658\)) with only two factors remains:

• A significant reduction in mean speed of 4.5 km/h is observed at the Swedish sites.

• 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).

The conclusions of the regression analysis support what was suggested in the exploratory analysis, concluding that, given that all sites in this study have identical posted speed limits, regional effects such as education, enforcement, or culture might be in play instead.

\label{tab:se_regression_mean_speed}

Yielding Post-Encroachment Time

A linear regression is performed on median \(yPET\) at each site (including only yPET below 5 s), to test all explainable differences between sites, as shown in Table \ref{tab:analysis_zones}. \(yPET\) observations are separated into lead \(yPET\)—between the road user already in the roundabout preceding the road user entering from the approach—and lag \(yPET\)—between the road user entering from the approach and the following road user already in the roundabout. The coefficients of regression, adjusted \(R^2\), Wald test score, and number of observations are provided in Table \ref{tab:se_regression_mean_speed}.

No suitable regression model is found for lead \(yPET\). Meanwhile, while Outside Radius and Flow are found to be associated with lag \(yPET\) with intuitive signs, having a moderately powerful relationship, region is not found to be significantly correlated with median lag \(yPET\) either.

Time-to-Collision

Given the hierarchical nature of the data, a random effects regression of motion pattern-based serious \(TTC_{15}\) (shorthand for \(TTC_{15^{th}cmp}\)) SCC events is performed, using the log of \(TTC_{15}\):

\[ln(TTC_{15_{ij}}) = \alpha + {\sum}_{k} ( \beta_k X_{kij} + u_{ik}) + u_{i} + \epsilon_{ij} \label{eq:se_ttc_regress_random_effects}\]

for \(j=1,...,m\) pairs of road users and for sites \(i=1,...,n\) (merging zones), where \(\alpha\) is the model intercept, \(\beta_k\) is the coefficient of factor \(X_{kij}\) for \(k=1,...,o\) factors, \(u_{i}\) is the approach-specific random error, and \(\epsilon_{ij}\) is the “ordinary” regression error.

Results of the regression are shown in Table \ref{tab:se_regression_ttc_continuum}. The regression yields a moderately predictive model with a \(R^2 = 0.425\) (which accounts for differences between merging zones). The difference in safety between sites seems to be in large part accounted for by the Swedish Site variable, as it is associated with an increase in expected \(TTC_{15}\) of 0.293 seconds, thus suggesting that sites located in Sweden benefit from a non-trivial reduction in collision probability. Construction year (or elapsed time since roundabout construction) is not found to be correlated significantly suggesting that, at this time scale at least, acclimatization to roundabouts is not a significant effect.

A very minor within-effect is also noted: fifteen-second-traffic-exposure being associated with an increase in \(TTC_{15}\) at a rate of 0.017 seconds per road user present within 15 seconds. This appears to be somewhat counterintuitive, but it might suggest that increasing driving complexity really does have a positive effect on increasing driver alertness. Furthermore, as evidenced with the angle of incidence parameter, interactions with a small angle of incidence, i.e. rear end conflicts, seem to be associated with lower \(TTC_{15}\) values than with a larger angle of incidence, i.e. side swipe conflicts.

\label{tab:se_regression_ttc_continuum}