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Publication Number: FHWARD03037
Date: May 2005 

Validation of Accident Models for IntersectionsFHWA Contact: John Doremi, PDF Version (1.61 MB)
PDF files can be viewed with the Acrobat® Reader® 2. VALIDATION OF ACCIDENT MODELS (Continuation)Table 79 shows the GOF measures for the original injury accident model (Variant 1) in the Vogt report applied to the Georgia data.^{(2)} The Pearson productmoment correlation coefficients were higher those for the TOTACC models, and the MPB, MAD, and MSPE per year squared were smaller than those for the TOTACC models. Table 79. Validation Statistics for INJACC Type IV Model Using Georgia Data
^{1} Used Variant 1, but PKLEFT1 was removed from the model by dividing by the exponential value of the coefficient of this variable times its average effect Figure 11 depicts the prediction performance of the original model for individual sites in the Georgia 0.05mile data. It is quite evident that the original model generally does not fit the Georgia data well, a finding that would have been expected on the basis of the low Pearson productmoment coefficients. Figure 11. Observed versus Predicted Accident Frequency: INJACC Intersection Related Injury Accident Model (INJACCI)The parameter estimates, their standard errors, and pvalues are given in table 80. As was the case for INJACC, all of the variables were insignificant for the Georgia data. The variable AADT2 was estimated with an opposite sign to that for the original model. The overdispersion values with the Georgia data were similar to that for the original model. Table 81 shows the GOF measures for the original intersection related injury accident model (Variant 1) in the Vogt report applied to the Georgia data.^{(2)} The Pearson productmoment correlation coefficient was similar to that for the TOTACCI model, but the MPB, MAD, and MSPE per year squared were smaller. Table 80. Parameter Estimates for INJACCI Type IV Model Using Georgia Data
^{1} Vogt, 1999, (p. 118) ^{2} PKLEFT1 was not included in the model ^{3} K: Overdispersion value ^{4} N/A: not available Table 81. Validation Statistics for INJACCI Type IV Model Using Georgia Data
^{1} Used Variant 1, but PKLEFT1 was removed from the model by dividing by the exponential value of the coefficient of this variable times its average effect Figure 12 depicts the prediction performance of the original model for individual sites in the Georgia 0.05mile data. It is quite evident that the original model generally does not fit the Georgia data well, a finding that would have been expected on the basis of the low Pearson productmoment coefficients. Figure 12. Observed versus Predicted Accident Frequency: INJACCI 2.5.5 Model VThe summary statistics of the variables used in this model are provided in table 82. PKLEFT2 and PKTRUCK were not included in the Georgia data. The summary statistics indicate that the Georgia intersections had fewer accidents, on average, than those in the original data. For example, about 10 percent of the Georgia sites did not have an accident during the period of 1996 and 1997, while all of the original sites experienced at least one accident. The majority of the Georgia sites did not have a protected leftturn lane on the major road (PROT_LT), while PROT_LT was present at almost a half of the sites in the original models. As mentioned previously, some of the data acquired did not exactly match the summary statistics given in the report.^{(2)} Specifically, there was a problem reproducing vertical alignment related variables: VEI1, VEI2, and VEICOM. Table 82. Summary Statistics of Georgia Data: Type V
^{1} Vogt, 1999, (p. 6164) ^{2} N/A: not available Separate summary statistics for three States, shown in table 83, were examined to see if there were differences in the variables between States. These summary statistics indicate that the Michigan sites had, on average, higher accident frequencies than California. They also reveal that the majority of the sites in California had protected leftturn lanes (PROT_LT=1), while the Michigan and Georgia data had no sites with this feature present. Table 83. Summary Statistics for Three States: California, Michigan, and Georgia^{1}
^{1} Summary Statistics for California and Michigan were produced using the obtained original data ^{2} N/A: not available Total Accident Models (TOTACC)Since the variables PKLEFT1 and PKTRUCK were not present in the Georgia data, modifications to the validation procedure had to be performed as described earlier. In the validation, the same parameter estimates in the originally original report were used, and the parameter estimates were also reproduced without PKLEFT1 and PKTRUCK for the revised original model. Two models (original model and revised original model) were used for the validation activity to determine GOF measures. For the original model, the same parameter estimates in the report were used. For the revised original model, since PKLEFT2 and PKTRUCK were not available in the Georgia data, these variables were removed from the original published model by dividing by the exponential value of their coefficients times their average effects, i.e., their average values. The validation addressed the main model and one variant. Main ModelThe model reestimation results are shown in table 84. For the revised original model, without the variables PKLEFT2 and PKTRUCK, the constant term and all of the variables were estimated with the same sign as the reported model, but all of them except PROT_LT were insignificant. The overdispersion parameter, K, was almost twice as high as that for the original model. For the Georgia data, the constant term, AADT1, AADT2, and VEICOM were estimated with the same sign as the reported model, but there were differences in magnitude. PROT_LT was estimated with an opposite sign, although it was statistically insignificant. AADT2 and VEICOM were also insignificant. The overdispersion parameter, K, was substantially higher than that for the original models. Table 84. Parameter Estimates for TOTACC Type V Model Using Georgia Data: Main Model
^{1} Vogt, 1999, (p. 122) ^{2} Coefficient estimates of the variables were reproduced without PKLEFT2 and PKTRUCK using the original data ^{3} K: Overdispersion value ^{4} N/A: not available The validation statistics are shown in table 85. The revised original model was estimated with the same Pearson productmoment correlation coefficient as that for the original model. The MPB per year was larger than that for the original model, while the MADs were similar. The MSE per year was slightly higher than that for the original model. The Pearson correlation coefficient for the Georgia data was relatively low, indicating a poor linear fit. A value of 0.18 of the Pearson correlation coefficient indicates that the accident predictions by the original model and the Georgia data are marginally correlated at best. The MPB and MAD per year were larger than those for the original models. The MSPEs per year squared were significantly higher than the MSEs per year squared, indicating a general lackoffit. Table 85. Validation Statistics for TOTACC Type V Model Using Georgia Data: Main Model
^{1} The original main model in the report. This model includes PKLEFT2 and PKTRUCK ^{2} Used the same coefficients in the original model, but PKLEFT2 and PKTRUCK were removed from the model by dividing by the exponential value of the coefficient of these variables times their average effects ^{3} N/A: not available Figure 13 depicts the prediction performance of the original model for individual sites in the Georgia 0.05mile data. It is quite evident that the original model generally does not fit the Georgia data well, a finding that would have been expected on the basis of the low Pearson productmoment coefficients. Variant 1The parameter estimates, their standard errors, and pvalues are given in table 86. In the revised original model, without the variables PKLEFT2 and PKTRUCK, the constant term, AADT1*AADT2 and PROT_LT were estimated with the same sign as the reported model, but there were differences in magnitude. The constant term and VEICOM were statistically insignificant. The overdispersion parameter, K, was almost twice as high as that for the original model. For the Georgia data, the constant term, AADT1*AADT2, and VEICOM were estimated with the same sign as the reported model, but the constant term and VEICOM were insignificant. PROT_LT was estimated with an opposite sign, but with similar degree of magnitude. The overdispersion parameter K was significantly higher than that for the original models. Figure 13. Observed versus Predicted Accident Frequency: TOTACC Main Model Table 86. Parameter Estimates for TOTACC Type V Model Using Georgia Data: Variant 1
^{1} Vogt, 1999, (p. 122) ^{2} Coefficient estimates of the variables were reproduced without PKLEFT2 and PKTRUCK using the original data ^{3} PKLEFT2 and PKTRUCK were not included in the model ^{4} K: Overdispersion value ^{5} N/A: not available The validation statistics are shown in table 87. For the revised original model the Pearson correlation coefficient was the same as that for the reported model. The MPB per year was larger than that for the original model, while the MADs and MSEs per year were similar. A value of 0.19 of the correlation coefficient indicates that the accident predictions by the original model and the Georgia data are marginally correlated at best. The MPBs and MAD per year was almost twice as large as those for the original model. The MSPEs per year squared were also significantly higher than the MSEs per year squared, indicating a general lackoffit. Table 87. Validation Statistics for TOTACC Type V Model Using Georgia Data: Variant 1
^{1} The Variant 1 in the report. This model includes PKLEFT2 and PKTRUCK ^{2} Used the same coefficients as Variant 1, but PKLEFT2 and PKTRUCK were removed from the model by dividing by the exponential value of the coefficient of these variables times their average effects ^{3} N/A: not available Figure 14 depicts the prediction performance of the original model for individual sites in the Georgia 0.05mile data. It is quite evident that the original model generally does not fit the Georgia data well, a finding that would have been expected on the basis of the low Pearson productmoment coefficients. Figure 14. Observed versus Predicted Accident Frequency: TOTACC Variant 1 Intersection Related Total Accident Model (TOTACCI)As before, since the variables PKLEFT1 and PKTRUCK were not present in the Georgia data, models were reestimated without PKLEFT1 and PKTRUCK for the revised original model. In addition, the estimation of GOF measures, used a revised original in which these variables were removed from the original published model by dividing by the exponential value of their coefficients times their average effects, i.e., their average values. The validation addresses the main model and one variant. Main ModelThe parameter estimates, their standard errors, and pvalues are given in table 88. In the revised original model all of the variables were estimated with the same direction of effect as for the original model, but there were sizeable differences in magnitude and significance. The estimates for all of the variables and the constant term were statistically insignificant. The overdispersion parameter, K, was somewhat higher than that for the original model. Table 88. Parameter Estimates for TOTACCI Type V Model Using Georgia Data: Main Model
^{1} Vogt, 1999, (p. 123) ^{2} Coefficient estimates of the variables were reproduced without PKLEFT2 and PKTRUCK using the original data ^{3} PKLEFT2 and PKTRUCK were not included in the model ^{4} K: Overdispersion value ^{5} N/A: not available For the Georgia data, the constant term, AADT1, AADT2, and VEICOM were estimated with the same sign as the reported model, but there were differences in the magnitude and significance. PROT_LT was estimated with an opposite sign, although it was statistically insignificant. AADT2 and VEICOM also became insignificant. The overdispersion parameters, K, are significantly higher than for the original models. The validation statistics are shown in table 89. The Pearson productmoment correlation coefficient of the revised original model was estimated to be the same as that for the original model. The MPB per year was somewhat larger, while the MAD per year was similar to that for the original model. The MSE per was higher than that for the original model, but the difference was not great. A value of 0.23 of the Pearson correlation coefficient indicates that the accident predictions by the original model are marginally linearly correlated with observed number of accidents in the 1996 to 1997 period. The MPB and MAD per year were larger than those for the original models. The MSPEs per year squared were significantly higher than the MSEs per year squared, indicating a general lackoffit. Figure 15 depicts the prediction performance of the original model for individual sites in the Georgia 0.05mile data. It is quite evident that the original model generally does not fit the Georgia data well, a finding that would have been expected on the basis of the low Pearson productmoment coefficients. Table 89. Validation Statistics for TOTACCI Type V Model Using Georgia Data: Main Model
^{1} The original main model in the report. This model includes PKLEFT2 and PKTRUCK ^{2} Used the same coefficients as the original model, but PKLEFT2 and PKTRUCK were removed from the model by dividing by the exponential value of the coefficient of these variables times their average effects ^{3} N/A: not available Figure 15. Observed versus Predicted Accident Frequency: TOTACCI Main Model Variant 3The parameter estimates, their standard errors, and pvalues are provided in table 90. In the revised original model all of the variables were estimated as insignificant, while only AADT2 was insignificant in the original model. There were also differences in the magnitude of the parameters. The overdispersion parameter, K, was almost twice as high as that for the original model. For the Georgia data, the constant term, AADT1, AADT2, and VEICOM were estimated with the same sign as the reported model, but there were slight differences in magnitude. PROT_LT and DRWY1 were estimated with an opposite sign to that in the original model, but these were insignificant. VEICOM was also insignificant. The overdispersion parameter K was significantly higher than that for the original model, indicating lackoffit to the Georgia data. Table 90. Parameter Estimates for TOTACC Type V Model Using Georgia Data: Variant 3
^{1} Vogt, 1999, (p. 123) ^{2} Coefficient estimates of the variables were reproduced without PKLEFT2 and PKTRUCK using the original data ^{3} PKLEFT2 and PKTRUCK were not included in the model ^{4} K: Overdispersion value ^{5} N/A: not available Table 91 shows the validation statistics. The Pearson productmoment correlation coefficient of the revised original model was estimated to be the same as the original model. The MPB and MAD per year were somewhat larger than for the original model. The MSE per was also higher than that for the original model. Table 91. Validation Statistics for TOTACCI Type V Model Using Georgia Data: Variant 3
^{1} Variant 3 in the report; this model includes PKLEFT2 and PKTRUCK ^{2} Used the same coefficients as Variant 3, but PKLEFT2 and PKTRUCK were removed from the model by dividing by the exponential value of the coefficient of these variables times their average effects ^{3} N/A: not available A value of 0.22 of the Pearson correlation coefficient indicates that the accident predictions by the original model are marginally linearly correlated with observed number of accidents in the 1996 to 1997 period. The MPBs and MADs per year for the Georgia data were larger than those for the original models. The MSPEs were also significantly higher than the MSEs, which suggests lackoffit to the Georgia data. Figure 16 depicts the prediction performance of the original model for individual sites in the Georgia 0.05mile data. It is quite evident that the original model generally does not fit the Georgia data well, a finding that would have been expected on the basis of the low Pearson productmoment coefficients. Figure 16. Observed versus Predicted Accident Frequency: TOTACCI Variant 3 Injury Accident Model (INJACC)The parameter estimates, their standard errors, and pvalues are provided in table 92. The models estimated with the Georgia data generally showed differences in sign, magnitude, and significance of the parameter estimates. PROT_LT and VEICOM were estimated with an opposite sign to those in the original model, although they were insignificant. The constant term and AADT1*AADT2 were estimated with the same direction of effect and in general a similar degree of magnitude and significance to the original model. The overdispersion parameter K was significantly higher than that for the original model. Table 93 shows the GOF measures for the original injury accident model in the Vogt report applied to the Georgia data.^{(2)} The Pearson productmoment correlation coefficient was similar to that for the TOTACC model. However, the MPB, MAD, and MSPE per year squared were smaller. Table 92. Parameter Estimates for INJACC Type V Model Using Georgia Data
^{1} Vogt, 1999, (p. 124) ^{2} PKLEFT2 and PKTRUCK were not included in the model ^{3} K: Overdispersion value S N/A: not available Table 93. Validation Statistics for INJACC Type V Model Using Georgia Data
^{1} Used the same coefficients as the original model, but PKLEFT2 and PKTRUCK were removed from the model by dividing by the exponential value of the coefficient of these variables times their average effects ^{2} K: Overdispersion value Figure 17 depicts the prediction performance of the original model for individual sites in the Georgia 0.05mile data. It is quite evident that the original model generally does not fit the Georgia data well, a finding that would have been expected on the basis of the low Pearson productmoment coefficients. Figure 17. Observed versus Predicted Accident Frequency: INJACC Intersection Related Total Injury Accident Model (INJACCI)The parameter estimates, their standard errors, and pvalues are provided in table 94. For the Georgia data, the constant term, AADT1*AADT2, and VEICOM were estimated with the same sign but with differences in magnitude and significance. The constant term and AADT1*AADT2 were estimated as significant, while they were insignificant in the original model. The overdispersion parameters, K, were significantly higher than that for the original model. Table 95 shows the GOF measures for the original intersection related injury accident model (Variant 1) in the Vogt report applied to the Georgia data.^{(2)} The Pearson productmoment correlation coefficient was slightly higher than for the TOTACCI model, and the MPB, MAD, and MSPE per year squared were smaller. Table 94. Parameter Estimates for INJACCI Type V Model Using Georgia Data
^{1} Vogt, 1999, (p. 124) ^{2} PKLEFT2 and PKTRUCK were not included in the model ^{3} K: Overdispersion value ^{4}N/A: not available Table 95. Validation Statistics for INJACC Type V Model Using Georgia Data
^{1} Used the same coefficients as the original model, but PKLEFT2 and PKTRUCK were removed from the model by dividing by the exponential value of the coefficient of these variables times their average effects ^{2} K: Overdispersion value Figure 18 depicts the prediction performance of the original model for individual sites in the Georgia 0.05mile data. It is quite evident that the original model generally does not fit the Georgia data well, a finding that would have been expected on the basis of the low Pearson productmoment coefficients. Figure 18. Observed versus Predicted Accident Frequency: INJACCI 