Area Type Sub Model Estimation Area Type Sub Model Estimation � AT classification used in: AT classification used in: � -Estimating highway capacities -Estimating highway capacities -Stratifying work trip attractions -Stratifying work trip attractions -Summarize results of mode choice model -Summarize results of mode choice model � Why Modeling AT? Why Modeling AT? � - Should be sensitive with the changes in future data - Should be sensitive with the changes in future data - Simple definitions not possible using individual zonal data Simple definitions not possible using individual zonal data -
Model Estimation Methodology Model Estimation Methodology � � “Model team” prepared a “Subjective” map “Model team” prepared a “Subjective” map - - Used as the “Target Map” Used as the “Target Map” � Area Types based on geography and local knowledge � Area Types based on geography and local knowledge - Rural Rural - -Urban -Urban -CBD -CBD � Assumptions in Model Estimation � Assumptions in Model Estimation - AT of a TAZ depends on the PD and ED and/or LOS - AT of a TAZ depends on the PD and ED and/or LOS -AT of a TAZ is related to surrounding zones -AT of a TAZ is related to surrounding zones
“Subjective” AT Map Winston-Salem Greensboro Burlington High Point Map layers TAZs without Lakes AT1 1 2 3 0 4 8 12 Miles
Original TAZ distributions TAZs plotted by pop and emp density 1000000.00 100000.00 10000.00 Rural 1000.00 ED Urban 100.00 CBD 10.00 1.00 1.00 10.00 100.00 1000.0 10000. 10000 0.10 0 00 0.00 PD
Model Estimation Methodology Contd. Model Estimation Methodology Contd. 530 454 � Need for considering the surrounding � Need for considering the surrounding 523 623 789 zones zones 640 634 � Which Surrounding zones need to be � Which Surrounding zones need to be 791 633 526 632 considered? considered? 636 638 626 725 � � 3 Approaches Tested 3 Approaches Tested 723 � � Zones within a distance specified by Zones within a distance specified by - User (X) - User (X) - A multiple (F) of Zonal Units (ZU), - A multiple (F) of Zonal Units (ZU), Where ZU = SQRT(A) Where ZU = SQRT(A) and and -Adjacent Zones (Physically touching) -Adjacent Zones (Physically touching)
Model Estimation Methodology Contd. Model Estimation Methodology Contd. � Which approach gives best results? � Which approach gives best results? - Approach 1: X is varied from 0.5 to 2.5 mi. @ 0.5 interval. Approach 1: X is varied from 0.5 to 2.5 mi. @ 0.5 interval. - -Approach 2: F is varied from 0.75 to 2 @ 0.25 interval -Approach 2: F is varied from 0.75 to 2 @ 0.25 interval -Approach 3: No variation -Approach 3: No variation � TAZs distributed graphically by W/ distributed graphically by W/Avg Avg. of PD and ED & observed . of PD and ED & observed � TAZs in GIS in GIS - - Better distribution of area types Better distribution of area types -Difficult to define AT -Difficult to define AT
Observed AT classification from Approach 2, F=1.5 Observed Area Type Classification 100000.00 10000.00 1000.00 Rural ED 100.00 Urban CBD 10.00 1.00 1.00 10.00 100.00 1000.00 10000.00 0.10 PD
Model Estimation Methodology Contd. Model Estimation Methodology Contd. � Need of a statistical analysis � Need of a statistical analysis � Discriminant Classification Test: Classification Test: � Discriminant - Target classes : Existing AT classes from “Subjective” map Target classes : Existing AT classes from “Subjective” map - Rural =1, Urban = 2, CBD=3 Rural =1, Urban = 2, CBD=3 - Variables used : PD and ED - Variables used : PD and ED - Results: - Results: – Classification function coefficients – Classification function coefficients – – Classification table Classification table – – Case wise representation of observed and predicted AT Case wise representation of observed and predicted AT � Classification tables compared for each approach Classification tables compared for each approach � � Approach 2 with F = 1.5 is selected to be the best for Triad � Approach 2 with F = 1.5 is selected to be the best for Triad
Discriminant Classification Results Table 2: AT classification using Approach 1, X = 0.5 Table 1: AT classification using PD and ED of individual TAZs Classification Table Classification Table Classification Table Classification Table Pred. Group Pred . Group Correctly Correctly Pred. Group Pred . Group Correctly Correctly Act. Group Act. Group 1 1 2 2 3 3 Classified Classified Act. Group Act. Group 1 1 2 2 3 3 Classified Classified 1 505 2 0 0.996 1 505 2 0 0.996 1 1 504 504 3 3 0 0 0.994 0.994 2 428 664 17 0.599 2 428 664 17 0.599 2 375 699 35 0.630 2 375 699 35 0.630 3 15 4 20 0.513 3 15 4 20 0.513 3 0 8 31 0.795 3 0 8 31 0.795 Overall Correct Class. Rate 0.718 Overall Correct Class. Rate 0.746 Overall Correct Class. Rate 0.718 Overall Correct Class. Rate 0.746 Table 3: AT classification using Approach 1, X = 1 Table 4: AT classification using Approach 1, X = 1.5 Classification Table Classification Table Classification Table Classification Table Pred. Group Pred . Group Correctly Correctly Pred. Group Pred . Group Correctly Correctly Act. Group Act. Group 1 1 2 2 3 3 Classified Classified Act. Group 1 2 3 Classified Act. Group 1 2 3 Classified 1 1 498 498 9 9 0 0 0.982 0.982 1 1 496 496 11 11 0 0 0.978 0.978 2 313 680 116 0.613 2 313 680 116 0.613 2 2 334 334 701 701 74 74 0.632 0.632 3 0 6 33 0.846 3 0 6 33 0.846 3 3 0 0 6 6 33 33 0.846 0.846 Overall Correct Class. Rate 0.732 Overall Correct Class. Rate 0.732 Overall Correct Class. Rate Overall Correct Class. Rate 0.743 0.743
Discriminant Classification Results Contd. Table 6: AT classification using Approach 1, X = 2.5 Table 5: AT classification using Approach 1, X = 2 Classification Table Classification Table Classification Table Classification Table Pred. Group . Group Correctly Pred Correctly Pred. Group Pred . Group Correctly Correctly Act. Group Act. Group 1 1 2 2 3 3 Classified Classified Act. Group Act. Group 1 1 2 2 3 3 Classified Classified 1 1 485 485 22 22 0 0 0.957 0.957 1 492 15 0 0.970 1 492 15 0 0.970 2 296 619 194 0.558 2 296 619 194 0.558 2 2 301 301 651 651 157 157 0.587 0.587 3 0 6 33 0.846 3 0 6 33 0.846 3 3 0 0 6 6 33 33 0.846 0.846 Overall Correct Class. Rate 0.687 Overall Correct Class. Rate 0.687 Overall Correct Class. Rate Overall Correct Class. Rate 0.711 0.711 Table 7: AT classification using Approach 2, F =0.75 Table 8: AT classification using Approach 2, F = 1.00 Classification Table Classification Table Classification Table Classification Table Pred. Group Pred . Group Correctly Correctly Pred. Group . Group Correctly Pred Correctly Act. Group Act. Group 1 1 2 2 3 3 Classified Classified Act. Group Act. Group 1 1 2 2 3 3 Classified Classified 1 1 503 503 3 3 1 1 0.992 0.992 1 1 499 499 8 8 0 0 0.984 0.984 2 2 422 422 670 670 17 17 0.604 0.604 2 2 393 393 697 697 19 19 0.628 0.628 3 3 12 12 6 6 21 21 0.538 0.538 3 3 5 5 10 10 24 24 0.615 0.615 Overall Correct Class. Rate Overall Correct Class. Rate 0.721 0.721 Overall Correct Class. Rate Overall Correct Class. Rate 0.737 0.737
Discriminant Classification Results Contd. Table 9: AT classification using Approach 2, F = 1.25 Table 10: AT classification using Approach 2, F =1.5 Classification Table Classification Table Classification Table Classification Table Pred. Group Pred . Group Correctly Correctly Pred. Group Pred . Group Correctly Correctly Act. Group Act. Group 1 1 2 2 3 3 Classified Classified Act. Group Act. Group 1 1 2 2 3 3 Classified Classified 1 1 502 502 5 5 0 0 0.990 0.990 1 1 500 500 7 7 0 0 0.986 0.986 2 360 734 15 0.662 2 361 735 13 0.663 2 360 734 15 0.662 2 361 735 13 0.663 3 2 9 28 0.718 3 0 9 30 0.769 3 2 9 28 0.718 3 0 9 30 0.769 Overall Correct Class. Rate 0.764 Overall Correct Class. Rate 0.764 Overall Correct Class. Rate 0.764 Overall Correct Class. Rate 0.764 Table 11: AT classification using Approach 2, F = 2 Table 12: AT classification using Approach 3 Classification Table Classification Table Classification Table Classification Table Pred. Group Pred . Group Correctly Correctly Pred. Group Pred . Group Correctly Correctly Act. Group Act. Group 1 1 2 2 3 3 Classified Classified Act. Group Act. Group 1 1 2 2 3 3 Classified Classified 1 1 499 499 8 8 0 0 0.984 0.984 1 1 499 499 8 8 0 0 0.984 0.984 2 404 693 12 0.625 2 404 693 12 0.625 2 362 733 14 0.661 2 362 733 14 0.661 3 1 13 25 0.641 3 1 13 25 0.641 3 0 10 29 0.744 3 0 10 29 0.744 Overall Correct Class. Rate 0.735 Overall Correct Class. Rate 0.735 Overall Correct Class. Rate 0.762 Overall Correct Class. Rate 0.762
Predicted AT Classification by Discriminant Analysis on Approach 2, F=1.5 Predicted Area Type Classification 100000.00 10000.00 1000.00 Rural 100.00 Urban ED CBD 10.00 1.00 1.00 10.00 100.00 1000.00 10000.00 0.10 PD
Difference between Predicted AT Map and Target Map AT-150 1 2 3 0 4 8 12 Miles
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