Safety Impacts and Other Implications of Raised Speed Limits on High-Speed Roads (2006)

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168 E Synthetic Speed Choice Model Data Section 4.2.5 discussed the development and analysis of a rational speed choice model based on the hypothesis that a driver chooses the speed that minimizes the generalized cost of travel, which includes the time cost, expected crash cost and expected legal cost components associated with driving at a particular speed. It was not possible to solve analytically the minimization problem resulting from this formulation, so a numerical approach was adopted. Two synthetic datasets were generated, in which each record consisted of specific values for each of the parameters and variables used in the model. For each record (i.e. each set of generated parameter and variable values), the optimum speed was then determined using the MATLAB software package (Mathworks Inc., 1992) and inserted in the corresponding dataset record. A regression analysis was then performed using these datasets to relate the optimum speed to the key explanatory variables. This appendix describes the generation of the two synthetic datasets used in the analysis of the rational speed choice model. E.1 Dataset 1 495,000 (= 10*10*10*9*11*5) data points were generated using assumed values for parameters and variables shown in Tables E-1 and E-2. Table E-3 presents descriptive statistics of the generated dataset. Table E-1 – Parameter Values Assumed for Generation of Dataset 1 Coefficients Assumed values Number of values tb0 0.01 1 tb1 0.01+0.005*N(0,1) 10 cb0 0.00033 1 cb1 0.000001 1 cb2 0.00000075+0.000000375*N(0,1) 10 ca0 500 1 ca1 5 1 lb0 0.0024 1 lb1 0.000001 1 lb2 0.000015+0.0000075*N(0,1) 10 ca0 10 1 ca1 8 1

169 Table E-2 –Variable Values Assumed for Generation of Dataset 1 Variables Assumed values Number of values WAGE ($/veh-h) 10 to 50 by increment 5 9 SSPD (mi/h) 70 to 120 by increment 5 11 SL (mi/h) 55 to 75 by increment 75 5 Table E-3 – Descriptive Statistics for Dataset 1 Variables N Minimum Maximum Mean Std. Dev. SPEED (mi/h) 495,000 59.1 100.3 78.1 9.5 WAGE ($/veh-h) 495,000 10.0 50.0 30.0 12.9 SSPD (mi/h) 495,000 70.0 120.0 95.0 15.8 SL (mi/h) 495,000 55.0 75.0 64.9 7.0 E.2 Dataset 2 1,856,250 (= 5*5*3*5*5*3*6*11*5) speed data points were generated using assumed values for parameters and variables shown in Tables E-4 and E-5. Table E-6 presents descriptive statistics of the generated dataset. Table E-4 – Parameter Values Assumed for Generation of Dataset 2 Coefficients Assumed values Number of values tb0 0.01 1 tb1 0.01+ 0013.0 *N(0,1) 5 cb0 0.00033 1 cb1 0.000001 1 cb2 0.00000075+ 010000000000.0 *N(0,1) 5 ca0 500 1 ca1 5+1*N(0,1) 3 lb0 0.0024 1 lb1 0.000001+ 000010.00000000 * N(0,1) 5 lb2 0.000015+ 00250.00000000 *N(0,1) 5 ca0 10 1 ca1 8+ 2 * N(0,1) 3 Note: The variances for generation were set for each coefficient not to change its sign.

170 Table E-5 –Variable Values Assumed for Generation of Dataset 2 Variables Assumed values Number of values WAGE ($/veh-h) 10 to 50 by increment 7 6 SSPD (mi/h) 70 to 120 by increment 5 11 SL (mi/h) 55 to 75 by increment 5 5 Table E-6 – Descriptive Statistics for Dataset 2 Variables N Minimum Maximum Mean Std. Dev. SPEED (mi/h) 1,856,250 59.3 104 80.0 10.3 WAGE ($/veh-h) 1,856,250 10 45 27.5 12.0 SSPD (mi/h) 1,856,250 70 120 95.0 15.8 SL (mi/h) 1,856,250 55 75 64.9 7.0