Summary and Discussions Sample Clauses

Summary and Discussions. Both qualitative (professional judgment and similar routes, etc.) and quantitative (elasticity analysis and econometric modeling, etc.) methods were proven useful in transit ridership forecasting, and many agencies employed multiple methods in their analysis. Among the quantitative methods, regional travel demand models remain a powerful tool to estimate transit share based on system characteristics, built environment, and the demographics and other contributing factors. These tools are usually readily available and provide a systematic and holistic view of travel choices. With recent advancements in activity-based modeling and better representation of land use factors at higher resolutions, these models may equip the agencies with better capabilities for transit analysis. However, since these regional models generally are not geared toward transit planning and service analysis, they may not be able to reflect the impacts of changes in the transit network or services on travel behavior to the full extent. Complexity of the regional model, cumbersome procedures, long run times, and lack of flexibility are the other common obstacles a transit agency may face. Consequently, local transit agencies were more likely to develop models at finer scales, such as route-level, stop-level, or segment-level ridership models. These tools would provide more user-friendly features that allow the transit agencies to explore and analyze various strategies and scenarios in transit service planning and operations. In this regard, regression models were the most widespread methodology for ridership estimation. This approach would also allow the analyst to take into account additional factors within the corridor or at the route or stop level that may have significant impacts on the usage of transit. On the other hand, it may also require the collection of additional data. Enhanced modeling techniques have also been proposed which tended to enhance the existing models either through the consideration of additional dimensions (geographically weighted regression models and time-series analysis, etc.) or better handling of the demand and supply (dynamic demand formulations and neural network, etc.). However, applying these methods in practice has not been well established at least in the United States, perhaps due to the complexity of the methods, or the data required for model calibration. There are several existing tools (such as, T-BEST and STOPS) that present great potential for...
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  • Results and Discussion Table 1 (top) shows the root mean square error (RMSE) between the three tests for different numbers of topics. These results show that all three tests largely agree with each other but as the sample size (number of topics) decreases, the agreement decreases. In line with the results found for 50 topics, the randomization and bootstrap tests agree more with the t-test than with each other. We looked at pairwise scatterplots of the three tests at the different topic sizes. While there is some disagreement among the tests at large p-values, i.e. those greater than 0.5, none of the tests would predict such a run pair to have a significant difference. More interesting to us is the behavior of the tests for run pairs with lower p-values. ≥ Table 1 (bottom) shows the RMSE among the three tests for run pairs that all three tests agreed had a p-value greater than 0.0001 and less than 0.5. In contrast to all pairs with p-values 0.0001 (Table 1 top), these run pairs are of more importance to the IR researcher since they are the runs that require a statistical test to judge the significance of the per- formance difference. For these run pairs, the randomization and t tests are much more in agreement with each other than the bootstrap is with either of the other two tests. Looking at scatterplots, we found that the bootstrap tracks the t-test very well but shows a systematic bias to produce p-values smaller than the t-test. As the number of topics de- creases, this bias becomes more pronounced. Figure 1 shows a pairwise scatterplot of the three tests when the number of topics is 10. The randomization test also tends to produce smaller p-values than the t-test for run pairs where the t- test estimated a p-value smaller than 0.1, but at the same time, produces some p-values greater than the t-test’s. As Figure 1 shows, the bootstrap consistently gives smaller p- values than the t-test for these smaller p-values. While the bootstrap and the randomization test disagree with each other more than with the t-test, Figure 1 shows that for a low number of topics, the randomization test shows less noise in its agreement with the bootstrap com- Figure 1: A pairwise comparison of the p-values less than 0.25 produced by the randomization, t-test, and the bootstrap tests for pairs of TREC runs with only 10 topics. The small number of topics high- lights the differences between the three tests. pared to the t-test for small p-values.

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