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69 Exhibit 78. Evaluation of Models Against Clip 56 Ratings. Clip 56 - Comparing LOS Distributions of Test Data and Models 4, 5 and 6 (N=50) - HCM LOS=4 60.00% 50.00% TEST MODEL 4 Probability Mass Function MODEL 5 MODEL 6 40.00% 30.00% 20.00% 10.00% 0.00% 1 2 3 4 5 6 LOS Rating (A=1; F=6) at each signal. In addition, it is a relatively clean and newly built AutoLOS = Mean (LOS) (Eq. 16) out area in the Washington, DC, suburb of Arlington, VA. This The average or "mean" LOS rating is the sum of the prob- combination of factors may have led participants to rate the abilities of an individual giving a facility a given LOS rating video higher, despite the overall low space mean speed of multiplied by the numerical equivalent of that LOS rating (J) 7.86mph and the high number of stops (6/mile). (worst = 1, best = 6). Comparing the mean LOS as observed, the HCM LOS, and the model performance for Models 4, 5, and 6 we find that the 6 Mean(LOS) = Pr(LOS = J )* J (Eq. 17) HCM overall tended to underpredict the mean LOS as J =1 observed in the video laboratories. Model 6 also tends to underpredict mean observed LOS. Where A correlation analysis of the various models and the test J = 1 for the worst LOS rating and 6 for the best LOS rating. dataset shows that Models 4, 5, and 6 all have superior corre- The Mean LOS number is converted to a mean letter grade lation to the mean video clip ratings than the HCM (see for the facility according to Exhibit 79. Exhibit 74). The numerical thresholds for converting the mean score to Essentially the models all show a positive correlation, in the mean LOS letter grade differ from the scores (J) used to that the compared models track the same in the positive or compute the mean score. Section 4.7 explained why different negative direction. The current HCM LOS method can only thresholds are used to convert the mean result to a letter explain approximately 46 percent of the variation in mean grade. observed LOS ratings. The three models developed for this The probability that a person will rate a given facility as exactly study all perform much better and can explain, on average, LOS J is computed by subtracting the cumulative probability of approximately 75 percent of the variation in mean observed LOS ratings. The best fitting model is Model 4, which uses Exhibit 79. Auto LOS Thresholds stops per mile, presence of an exclusive left-turn lane and the for Mean Numerical Scores. presence of trees to estimate the observed LOS ratings. LOS Mean Numerical Score A 2.00 5.2 Recommended Auto LOS Model B >2.00 and 2.75 C >2.75 and 3.50 The recommended auto LOS model (Model 6 above) pre- D >3.50 and 4.25 dicts the average degree of satisfaction rating for the facility, E >4.25 and 5.00 where LOS A is "very satisfied" and LOS F is "very dissatisfied." F > 5.00
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70 giving the facility a lower LOS rating from the cumulative prob- Model 1 provides a greatly superior statistical fit with the ability of giving the facility a LOS J rating or worse. video lab data, however; this model does not produce LOS Pr(LOS = J) = Pr(LOS J) - Pr(LOS J - 1) (Eq. 18) A for the streets contained in the video lab sample. Model 2 provides an inferior statistical fit with the data, but provides The probability that a person will rate a given facility as numerous LOS A results for the streets in the video lab sam- LOS J or worse is given by the ordered cumulative logit model ple. Both models predict LOS F for one or more of the streets as shown below: in the video lab sample. 1 The attribute, stops per mile, is the number of times a ve- Pr(LOS J ) = (Eq. 19) 1 + exp(-( J ) - k x k ) hicle decelerates from a speed above 5 mph to a speed below k 5 mph, divided by the length of the urban street segment under consideration. Where The attribute, Left-Turn-Lane Presence, takes on the fol- Pr(LOS<=J) = Probability that an individual will respond lowing values: with a LOS grade J or worse. exp = Exponential function. · 1 if exclusive left-turn lane at intersections, J = Alpha, Maximum numerical threshold for · 0 if not. LOS grade J (see Exhibit 80). K = Beta, Calibration parameters for attributes If the exclusive left-turn lanes do not provide sufficient (see Exhibit 80). storage for left-turning vehicles, then the number of stops per XK = Attributes (k) of the segment or facility (see mile would be affected, which would, in turn, adversely affect Exhibit 80). the perceived level of service. Two ordered cumulative logit models are recommended, The attribute, Percent Speed Limit, is the ratio of the actual both using the same form. average speed (distance traveled divided by the average travel Model 1, derived from a statistical analysis of the video lab time for the length of the arterial including all delays) to the data, predicts auto LOS as a function of the number of stops posted speed limit for the street. per mile and the presence of exclusive left-turn lanes. The attribute, Median Type, is equal to Model 2 was created to provide a speed-based model op- tion for auto LOS. Model 2 predicts auto LOS as a function of · 0 if no median, the percent of free-flow speed and the type of median. The · 1 if one-way street, parameters for this model were first derived statistically from · 2 if a painted median is present, and the video lab data. The resulting model, however, did not · 3 if a raised median is present. produce a full LOS A to LOS F range of results for the streets in the video lab sample. Given that public agencies may be re- The threshold values, j, and the attribute equation coeffi- luctant to adopt a LOS model that cannot predict LOS A, the cients, k, of the ordered cumulative logit function are LOS intercept values for the model were modified manually calibrated using the maximum likelihood estimation (MLE) to obtain a full LOS range of results for the streets in the video process applied to paired data of facility characteristics and clip sample while attempting to maintain as high a match per- perceived LOS collected from people participating in the centage with the video lab results as possible. video laboratory surveys. Exhibit 80. Alpha and Beta Parameters for Recommended Auto LOS Models. Parameter Model 1 Model 2 Alpha Values Intercept LOS E = -3.8044 1.00 Intercept LOS D = -2.7047 2.00 Intercept LOS C = -1.7389 2.50 Intercept LOS B = -0.6234 3.00 Intercept LOS A = 1.1614 4.00 Beta Values Stops/Mile= 0.2530 N/A Left-Turn-Lane Presence (0-1), = -0.3434 N/A Percent Speed Limit N/A -5.74 Median Type (0,1, 2, 3) N/A -0.39