                                                                               
                                                                               
                                                                          LBNL-

                                       
                                       
                                       
                                       
Assessment of DRI's Two-Stage Logistic Regression Model Used to Simultaneously Estimate the Relationship between Vehicle Mass or Size Reduction and U.S. Fatality Risk, Crashworthiness/Compatibility, and Crash Avoidance


Draft report prepared for the Office of Energy Efficiency and Renewable Energy, 
                            US Department of Energy
                                       
                                       
                                       
                                       
                                  Prepared by
                                       
                                  Tom Wenzel
               Building Technology and Urban Systems Department
                           Energy Technologies Area
                     Lawrence Berkeley National Laboratory
                              Berkeley, CA 94720
                                       
                                       
                                       
                                       
                                       

                                       
                                       
                                       
                                       
                                       
                                 January 2013
                                       
         This work was supported by the Vehicle Technologies Program, 
Office of Energy Efficiency and Renewable Energy of the U.S. Department of Energy 
                     under Contract No. DE-AC02-05CH11231.


Executive summary

1. Introduction

Reducing vehicle mass is perhaps the easiest and least-costly method to reduce fuel consumption and greenhouse gas emissions from light-duty vehicles.  However, the extent to which government regulations should encourage manufacturers to reduce vehicle mass depends on what effect, if any, light-weighting vehicles is expected to have on societal safety.  As part of an interagency analysis effort between the National Highway Traffic Safety Administration (NHTSA), the Environmental Protection Agency (EPA), and the Department of Energy (DOE), Lawrence Berkeley National Laboratory (LBNL) has been examining the relationship between vehicle mass and size and U.S. societal fatality and casualty risk, using historical data on recent vehicle designs.  This research effort informs the agencies on the extent to which vehicle mass can be reduced in order to meet fuel economy and greenhouse gas emissions standards, without compromising the safety of road users.

In 2012 NHTSA updated its 2003 and 2010 logistic regression analyses of the effect a reduction in light-duty vehicle mass has on US societal fatality risk per vehicle mile of travel (VMT; Kahane 2012); the 2012 analysis is the most thorough investigation of this issue to date.  In 2012 LBNL completed two studies that replicated NHTSA's analysis of fatality risk per VMT (Wenzel 2012a) and analyzed the relationship between mass reduction and the two components of risk per VMT, crashes per VMT (or crash frequency) and risk once a crash has occurred (or crashworthiness; Wenzel 2012b).

Dynamic Research, Inc. (DRI) released three reports in 2012 analyzing the relationship between vehicle mass and size and societal U.S. fatality risk.  The three DRI reports use essentially the same data and methodology developed by NHTSA to estimate the effect of a reduction in vehicle mass on societal fatality risk per VMT, while holding vehicle size (footprint) constant.  The Phase I DRI report attempts to identify, and correct, discrepancies in the data and methodology used to replicate the 2003 NHTSA results, for MY91 to MY99 vehicles in calendar years 1995 to 2000; however, DRI was not able to exactly replicate NHTSA's estimated effect of mass or footprint reduction on fatality risk per VMT.  In its Phase I report DRI also introduces a 2-stage regression model that simultaneously estimates the effect of mass or footprint reduction on the two components of fatality risk per VMT: crash frequency (crashes per VMT) and crashworthiness/compatibility (fatalities per crash).  The estimated effect of mass or footprint reduction on fatality risk per VMT from DRI's 2-stage model is quite similar to its estimates from its 1-stage model, but differences with NHTSA's 1-stage model remain.  The Phase II DRI report replicates the 2012 NHTSA results, for MY00 to MY07 vehicles in calendar year 2002 to 2008, and updates DRI's 2-stage regression model.  DRI was able to exactly replicate NHTSA's results for fatality risk per VMT in its 1-stage model, most likely because DRI used the same datasets as NHTSA, DRI's estimates for fatality risk per VMT in its 1- and 2-stage models in its Phase II report are quite similar. The Supplemental DRI report assesses the sensitivity of the regression estimates to two changes in the NHTSA methodology: using stopped, instead of non-culpable, vehicles in two-vehicle crashes as the measure of induced exposure, and replacing footprint with vehicle wheelbase and track width as the measure of vehicle size.  

This report summarizes LBNL's effort to replicate the DRI 2-stage regression model, and its results.

2. Classification of crash types

DRI used the databases of FARS fatality cases and 13-state induced exposure crash data that NHTSA developed for their 2012 report.  However, DRI used police-reported crash data from only 10 states (all the NHTSA states except AL, NJ, and WI) to estimate the effect of mass reduction on police-reported non-fatal crashes per VMT and fatalities per police-reported non-fatal crashes.  In addition, DRI used its own methodology to classify the state crash data by type of crash.  For its 2012 Phase 2 report, LBNL used the same 13 states as NHTSA, but also had to classify crashes by type using its own definitions.  In order to replicate DRI's Phase 2 analysis LBNL needs to reconcile the DRI and LBNL distributions of crashes by type, to determine whether the classification schemes are similar. 

Table 1 compares the total number of vehicles in non-fatal crashes in the 10 states reported by DRI (in Appendix E.f of DRI's Phase II report) and LBNL.  The table indicates that LBNL identified almost 4% more cars in non-fatal crashes in the 10 states than DRI; the biggest increases were in PA and MI, while LBNL identified substantially fewer cars in non-fatal crashes than DRI in WA, FL, MO, and NE.  The table indicates that these trends are consistent for light trucks and CUVs/minivans, as well as cars.  It is not clear why LBNL identified more vehicles involved in non-fatal crashes from the state data than DRI; one potential reason is that DRI excluded vehicles that had a reported model year prior to 1981 in the state crash databases.  Another possibility is differences in the programming DRI and LBNL used to decode vehicle identification numbers (VINs).

Table 2 shows the number of police-reported non-fatal crashes in PA, from Appendix E.f in DRI, by crash type and calendar year (2002 crash data for PA are unavailable).  Starting in 2006 DRI's count of crashes is one-third of their count in 2005; since this is consistent across all types of crashes Table 2 suggests there is an error in how DRI classified vehicles after 2005 in PA (PA did change the coding of their crash databases in 2006, which may be another source of the problem).

Table 3 compares the total number of vehicles in non-fatal crashes in the 10 states reported by DRI and LBNL, by vehicle and crash type.  LBNL identifies substantially more cars involved in rollovers and crashes with a heavy-duty truck and a light-duty truck, but substantially fewer cars involved in a crash with a heavier-than-average car, than DRI.  The majority of the discrepancy in Table 3 is for case vehicles involved in crashes with heavier-than-average cars and lighter-than-average light trucks; this suggests that either DRI and LBNL are using different average curb weights to define lighter- and heavier-than-average cars and light trucks, or DRI is classifying certain light truck models as cars (or alternatively LBNL is classifying certain car models as light trucks).  These trends are consistent for light trucks and CUVs/minivans as well.  

Table 1. Distribution of vehicles in police-reported non-fatal crashes, by state and vehicle type 
Vehicle type
State
                                                                            DRI
                                                                           LBNL
                                                                     Difference
                                                             Percent difference
Cars
FL
                                                                        498,430
                                                                        486,214
                                                                        -12,216
                                                                          -2.5%

KS
                                                                        109,023
                                                                        108,039
                                                                           -984
                                                                          -0.9%

KY
                                                                        268,576
                                                                        266,731
                                                                         -1,845
                                                                          -0.7%

MD
                                                                        214,641
                                                                        215,246
                                                                            605
                                                                           0.3%

MI
                                                                        474,921
                                                                        485,384
                                                                         10,463
                                                                           2.2%

MO
                                                                        325,618
                                                                        314,076
                                                                        -11,542
                                                                          -3.5%

NE
                                                                         77,786
                                                                         71,630
                                                                         -6,156
                                                                          -7.9%

PA
                                                                        116,391
                                                                        246,054
                                                                        129,663
                                                                         111.4%

WA
                                                                        201,910
                                                                        182,052
                                                                        -19,858
                                                                          -9.8%

WY
                                                                         13,839
                                                                         14,114
                                                                            275
                                                                           2.0%

Total
                                                                      2,301,135
                                                                      2,389,540
                                                                         88,405
                                                                           3.8%
Light trucks
FL
                                                                        280,020
                                                                        270,673
                                                                         -9,347
                                                                          -3.3%

KS
                                                                         75,908
                                                                         74,143
                                                                         -1,765
                                                                          -2.3%

KY
                                                                        171,910
                                                                        169,073
                                                                         -2,837
                                                                          -1.7%

MD
                                                                         88,628
                                                                         92,170
                                                                          3,542
                                                                           4.0%

MI
                                                                        359,487
                                                                        366,443
                                                                          6,956
                                                                           1.9%

MO
                                                                        194,313
                                                                        186,977
                                                                         -7,336
                                                                          -3.8%

NE
                                                                         52,845
                                                                         47,211
                                                                         -5,634
                                                                         -10.7%

PA
                                                                         58,802
                                                                        119,996
                                                                         61,194
                                                                         104.1%

WA
                                                                        114,969
                                                                        105,267
                                                                         -9,702
                                                                          -8.4%

WY
                                                                         19,829
                                                                         19,965
                                                                            136
                                                                           0.7%

Total
                                                                      1,416,711
                                                                      1,451,918
                                                                         35,207
                                                                           2.5%
CUVs/ minivans
FL
                                                                        110,801
                                                                        107,778
                                                                         -3,023
                                                                          -2.7%

KS
                                                                         28,747
                                                                         28,384
                                                                           -363
                                                                          -1.3%

KY
                                                                         64,549
                                                                         63,562
                                                                           -987
                                                                          -1.5%

MD
                                                                         48,530
                                                                         47,780
                                                                           -750
                                                                          -1.5%

MI
                                                                        171,976
                                                                        175,052
                                                                          3,076
                                                                           1.8%

MO
                                                                         76,563
                                                                         73,519
                                                                         -3,044
                                                                          -4.0%

NE
                                                                         21,546
                                                                         19,858
                                                                         -1,688
                                                                          -7.8%

PA
                                                                         28,266
                                                                         65,320
                                                                         37,054
                                                                         131.1%

WA
                                                                         56,489
                                                                         50,155
                                                                         -6,334
                                                                         -11.2%

WY
                                                                          3,562
                                                                          3,623
                                                                             61
                                                                           1.7%

Total
                                                                        611,029
                                                                        635,031
                                                                         24,002
                                                                           3.9%

Table 2. Distribution of PA non-fatal crashes by type and year

Crash type
                                                                           2003
                                                                           2004
                                                                           2005
                                                                           2006
                                                                           2007
                                                                           2008
                                                                          Total
DRI
Rollover
                                                                            153
                                                                            169
                                                                            192
                                                                             81
                                                                            102
                                                                            116
                                                                            813

Fixed object
                                                                          3,760
                                                                          4,855
                                                                          4,837
                                                                          2,531
                                                                          3,444
                                                                          4,150
                                                                         23,577

Ped etc.
                                                                            570
                                                                            813
                                                                            792
                                                                            151
                                                                            195
                                                                             13
                                                                          2,534

HDT
                                                                            692
                                                                            737
                                                                            872
                                                                            272
                                                                            366
                                                                            345
                                                                          3,284

Lgt car
                                                                          4,766
                                                                          6,448
                                                                          5,729
                                                                          1,717
                                                                          1,809
                                                                          1,866
                                                                         22,335

Hvy car
                                                                          3,598
                                                                          5,373
                                                                          5,390
                                                                          1,599
                                                                          2,030
                                                                          2,030
                                                                         20,020

Lgt LT
                                                                          1,754
                                                                          2,363
                                                                          1,966
                                                                            642
                                                                            704
                                                                            642
                                                                          8,071

Hvy LT
                                                                          1,211
                                                                          1,845
                                                                          1,891
                                                                            589
                                                                            794
                                                                            784
                                                                          7,114

Other
                                                                          5,629
                                                                          8,162
                                                                          8,039
                                                                          2,087
                                                                          2,303
                                                                          2,423
                                                                         28,643

Total
                                                                         22,133
                                                                         30,765
                                                                         29,708
                                                                          9,669
                                                                         11,747
                                                                         12,369
                                                                        116,391
LBNL
Rollover
                                                                            619
                                                                            690
                                                                            920
                                                                            965
                                                                          1,163
                                                                          1,274
                                                                          5,631

Fixed object
                                                                          4,735
                                                                          5,483
                                                                          6,518
                                                                          6,976
                                                                          8,693
                                                                          9,486
                                                                         41,891

Ped etc.
                                                                            633
                                                                            728
                                                                            842
                                                                            925
                                                                          1,048
                                                                          1,110
                                                                          5,286

HDT
                                                                            764
                                                                            942
                                                                          1,102
                                                                          1,273
                                                                          1,565
                                                                          1,411
                                                                          7,057

Lgt car
                                                                          5,821
                                                                          7,034
                                                                          7,374
                                                                          8,119
                                                                          8,437
                                                                          7,736
                                                                         44,521

Hvy car
                                                                          3,527
                                                                          4,493
                                                                          5,076
                                                                          5,880
                                                                          6,722
                                                                          6,157
                                                                         31,855

Lgt LT
                                                                          3,325
                                                                          4,108
                                                                          4,340
                                                                          5,239
                                                                          5,849
                                                                          5,153
                                                                         28,014

Hvy LT
                                                                          1,621
                                                                          2,217
                                                                          2,798
                                                                          3,485
                                                                          4,313
                                                                          3,958
                                                                         18,392

Other
                                                                          7,660
                                                                          9,221
                                                                         10,304
                                                                         11,206
                                                                         12,019
                                                                         12,997
                                                                         63,407

Total
                                                                         28,705
                                                                         34,916
                                                                         39,274
                                                                         44,068
                                                                         49,809
                                                                         49,282
                                                                        246,054


Table 3. Distribution of vehicles in police-reported non-fatal crashes, by vehicle and crash type
Vehicle type
Crash type
                                                                            DRI
                                                                           LBNL
                                                                     Difference
                                                             Percent difference
Cars
Rollover
                                                                         17,967
                                                                         21,424
                                                                          3,457
                                                                          19.2%

Fixed object
                                                                        213,292
                                                                        215,567
                                                                          2,275
                                                                           1.1%

Ped etc.
                                                                         42,685
                                                                         41,049
                                                                         -1,636
                                                                          -3.8%

HDT
                                                                         65,509
                                                                         88,528
                                                                         23,019
                                                                          35.1%

Lgt car
                                                                        389,037
                                                                        397,003
                                                                          7,966
                                                                           2.0%

Hvy car
                                                                        437,351
                                                                        341,056
                                                                        -96,295
                                                                         -22.0%

Lgt LT
                                                                        191,132
                                                                        299,889
                                                                        108,757
                                                                          56.9%

Hvy LT
                                                                        188,499
                                                                        214,763
                                                                         26,264
                                                                          13.9%

Other
                                                                        755,663
                                                                        770,261
                                                                         14,598
                                                                           1.9%

Total
                                                                      2,301,135
                                                                      2,389,540
                                                                         88,405
                                                                           3.8%
Light trucks
Rollover
                                                                         33,518
                                                                         37,837
                                                                          4,319
                                                                          12.9%

Fixed object
                                                                        148,346
                                                                        144,124
                                                                         -4,222
                                                                          -2.8%

Ped etc.
                                                                         23,774
                                                                         22,217
                                                                         -1,557
                                                                          -6.5%

HDT
                                                                         36,459
                                                                         48,587
                                                                         12,128
                                                                          33.3%

Lgt car
                                                                        232,596
                                                                        233,226
                                                                            630
                                                                           0.3%

Hvy car
                                                                        265,810
                                                                        202,715
                                                                        -63,095
                                                                         -23.7%

Lgt LT
                                                                        114,601
                                                                        177,621
                                                                         63,020
                                                                          55.0%

Hvy LT
                                                                        114,056
                                                                        127,443
                                                                         13,387
                                                                          11.7%

Other
                                                                        447,551
                                                                        458,148
                                                                         10,597
                                                                           2.4%

Total
                                                                      1,416,711
                                                                      1,451,918
                                                                         35,207
                                                                           2.5%
CUVs/ minivans
Rollover
                                                                          5,048
                                                                          5,744
                                                                            696
                                                                          13.8%

Fixed object
                                                                         37,270
                                                                         37,024
                                                                           -246
                                                                          -0.7%

Ped etc.
                                                                         11,453
                                                                         11,003
                                                                           -450
                                                                          -3.9%

HDT
                                                                         15,330
                                                                         21,352
                                                                          6,022
                                                                          39.3%

Lgt car
                                                                        104,989
                                                                        107,891
                                                                          2,902
                                                                           2.8%

Hvy car
                                                                        122,373
                                                                         93,400
                                                                        -28,973
                                                                         -23.7%

Lgt LT
                                                                         50,933
                                                                         82,329
                                                                         31,396
                                                                          61.6%

Hvy LT
                                                                         51,772
                                                                         59,914
                                                                          8,142
                                                                          15.7%

Other
                                                                        211,861
                                                                        216,374
                                                                          4,513
                                                                           2.1%

Total
                                                                        611,029
                                                                        635,031
                                                                         24,002
                                                                           3.9%

3. Comparison with results in DRI's Phase II report and LBNL sensitivities 

DRI decimated the state police-reported crash data "due to memory limitations in the Fortran software."  To accomplish this DRI randomly sampled 15 police-reported non-fatal crashes for each fatal FARS crash in the 10 states, for each combination of state, calendar year, and crash type. (For CUVs/minivans, DRI sampled 50 police-reported non-fatal crashes for each fatal FARS crash.)  This resulted in a random sample of 9%, 12%, and 24% of cars, light trucks, and CUVs/minivans, respectively, involved in non-fatal crashes in the state databases, with the same distribution by state, calendar year, and crash type as the number of FARS cases.  While this approach attempts to correct for differences in reporting thresholds, and reporting bias, across states, it may result in biased regression estimates if the samples are not randomly selected from all available vehicles.  

In order to test the sensitivity of the regression estimates to which vehicles happened to be randomly sampled, LBNL replicated DRI's approach and sampled a similar number of vehicles.  However, since LBNL could not replicate DRI's classification of vehicles by crash type, the total number of vehicles LBNL sampled differs somewhat from the number DRI sampled. Table 4 shows the number of cases DRI used in their 2012 Phase II report, the target sample based on DRI's method and LBNL's counts of vehicles, and the actual cases LBNL used in their first sensitivity analysis.  Table 4 also shows the number of cases LBNL used in a second sensitivity, which it sampled a second set of vehicles.  To the extent possible, the vehicles included in the alternative LBNL decimation case were different from those used in the initial decimation case.  If the actual number of non-fatal police-reported crashes for a given state, calendar year, and crash type was more than twice the target number desired, there is no overlap in the vehicles actually sampled under the two cases.  However, where the target sample exceeded the number available, the vehicles sampled in each case are exactly the same.  

Table 4.  Number of vehicles involved in non-fatal crashes used in regression analyses
Vehicle type
                                                          Actual cases DRI used
                                 Target sample based on DRI method, LBNL counts
                                               Actual cases LBNL used (model 1)
                                           LBNL model 2: Alternative decimation
Car
                                                                        201,735
                                                                        203,799
                                                                        206,005
                                                                        204,018
Light truck
                                                                        172,384
                                                                        172,005
                                                                        172,847
                                                                        172,467
CUV/minivan
                                                                        146,358
                                                                        152,576
                                                                        153,111
                                                                        152,676
Total
                                                                        520,477
                                                                        528,380
                                                                        531,963
                                                                        529,161

If possible, sampling should be avoided, as it may introduce bias in the estimates and reduce the explanatory power of the regression model. In addition, DRI's decimation method assumes that fatality rates (i.e. number of fatalities per crash) are constant across crash types.  Some types of crashes, especially rollovers and crashes with pedestrians/cycles/motorcycles, have higher societal fatality rates per crash than others.  This approach also does not allow for differences in fatality rates per crash among states that may not be accounted for in the other control variables NHTSA used (driving at night, on high-speed roads, in rural areas, and in high-fatality states). 

On the other hand, when using all of the police-reported crash data one must account for differences in reporting thresholds, and reporting bias, among the states.  A better approach than DRI's decimation method may be to use all of the non-fatal police-reported crash data, while including internal control variables for each state to control for differences in reporting thresholds, and reporting bias, among states. 

Table 5 shows the number of vehicles LBNL used in its three alternative models 3 through 5.  Model 3 applies DRI's decimation and sampling method to all 13 states included in the NHTSA analysis (as mentioned above, DRI was not able to obtain police-reported crash data for AL, NJ, and WI).  This provides a total of over 670,000 vehicles for analysis, a 25 percent increase from the sample DRI used from the 10 states.  Model 4 uses all crash data from the 13 states, and includes an internal control variable for each of the states except Florida.  This method increases the number of vehicles used by an order of magnitude, to over 6.4 million.  In model 5 LBNL replicates the data that NHTSA used in its analysis, by using "synthetic" data for the four state/CY combinations where police-reported crash data were not available (PA in 2002, MI in 2002 and 2003, and WY in 2008).  Following NHTSA's example, LBNL duplicated the crash data from the most recent year of available data (PA in 2003, MI in 2004, and WY in 2007).  In addition, for model 5 LBNL excluded all vehicles whose reported model year in the state crash data did not match the model year from the decoded VIN, as NHTSA did in their analysis (all data from WA were used in model 5, as WA does not report the vehicle model year in its police-reported crash database).  The combination of these two changes results in slightly higher number of vehicles used in LBNL model 5 than in model 4, as shown in Table 5.

Table 5.  Number of vehicles involved in non-fatal crashes used in LBNL regression analyses
Vehicle type
                                       LBNL model 3: Decimation using 13 states
                                    LBNL model 4: All crash data from 13 states
LBNL model 5: All crash data from 13 states, duplicate data for missing states/CY, only vehicles whose reported MY matches VIN
Car
                                                                        262,628
                                                                      3,480,677
                                                                      3,485,912
Light truck
                                                                        216,662
                                                                      2,020,045
                                                                      2,043,807
CUV/minivan
                                                                        191,104
                                                                        925,558
                                                                        934,785
Total
                                                                        670,394
                                                                      6,426,280
                                                                      6,464,504

Tables 6 through 8 show compare the estimated effect of mass or footprint reductions on U.S. societal fatality risk per crash, crash frequency per VMT, and societal fatality risk per VMT, respectively, from the NHTSA 2012 and DRI 2012 reports with LBNL's five alternate regression models.  The DRI estimates for footprint reduction in Tables 6 through 8 are the average estimates for footprint reduction in lighter- and heavier-than-average cars and light trucks, weighted by the number of fatalities, as reported in DRI 2012.

Table 6 compares the DRI and LBNL 2-stage estimates on the effect on fatality risk per crash (crashworthiness and crash compatibility).  LBNL model 1 predicts results similar to those for DRI only for mass reduction in heavier-than-average light trucks and footprint reductions in CUVs/minivans.  LBNL model 1 predicts a higher, and statistically significant, increase in fatality risk per crash in heavier-than-average cars, but substantially higher decreases in fatality risk per crash in lighter-than-average light trucks and CUVs/minivans, than DRI.  In addition LBNL model 3 estimates a smaller decrease than DRI in fatality risk per crash from footprint reduction in light trucks.

LBNL model 2 shows the sensitivity of the estimates to the particular vehicles that are included in the decimated sample.  LBNL's estimates are nearly identical for mass reduction in heavier-than-average cars CUVs/minivans, and footprint reduction in CUVs/minivans; however, the alternate data decimation results in substantially different estimates for the effect of mass or footprint reduction in light trucks.  In some cases estimates in LBNL model 2 are more similar to DRI's estimates than those in LBNL model 1.  The comparison of LBNL models 1 and 2 indicates that the particular vehicles included in the decimation sample may bias the regression model estimates.

LBNL model 3 shows the sensitivity of the estimates to including the three additional states used in NHTSA's analysis (AL, NJ, and WI).  Including the three additional states increases the estimated beneficial effect of mass reduction in lighter-than-average cars on fatality risk per crash, to a statistically-significant 0.55%.  LBNL model 3 reduces the estimated beneficial effect of mass reduction on lighter-than-average light trucks and CUVs/minivans; these estimates are closer to DRI's estimates.  In terms of footprint reduction, LBNL model 3 estimates a small (0.57%), but statistically-significant, increase in fatality risk per crash in cars, and a slightly smaller increase in fatality risk per crash in CUVs/minivans than in LBNL models 1 and 2 (1.49% vs. 1.65% and 1.60%).  

LBNL model 4 shows the sensitivity of the estimates to including all of the state crash data, rather than a decimation sample.  The regression model includes an internal control variable for each state, except Florida, to account for differences in reporting thresholds and bias across the states.  Estimates from LBNL model 4 are comparable to those from model 3 only for mass reductions in lighter-than average cars and light trucks.  LBNL model 4 estimates a substantially higher beneficial effect on risk per crash from mass reduction in heavier-than-average light trucks and CUVs/minivans, a smaller beneficial effect on risk per crash from footprint reduction in light trucks, and substantially higher detrimental effects on risk per crash from footprint reduction in cars and CUVs/minivans.

LBNL model 5 includes duplicated data for the four state/CY combinations for which data were not available, and excludes vehicles where the model year reported in the state crash data did not match the decoded VIN.  In most cases, these changes result in only small differences from the estimates in model 4; however, model 5 now estimates a relatively large (1.12%), and statistically-significant, reduction in fatality risk per crash from mass reduction in heavier-than-average cars, a large increases in risk per crash from footprint reduction in cars (1.25%) and CUVs/minivans (2.57%).

Table 6. DRI 2-stage and alternate LBNL 2-stage estimates of the effect of mass or footprint reduction on U.S. societal fatality risk per crash (crashworthiness/compatibility)
Variable
Case vehicle type
A. NHTSA 1-stage estimate
(fatalities per crash)
B. DRI 2-stage estimate (fatalities per crash)
          C. Alternate LBNL 2-stage estimates (fatalities per crash)




1. 10 states, 
decimated crash data
2. 10 states, alternate decimated crash data
3.13 states, 
decimated crash data
4. 13 states, 
all crash data 
5. 13 states, all crash data, duplicated data, where MY matches
Mass
reduction
Cars < 3106 lbs
                                       -- 
                                    -0.51%
                                    -0.35%
                                    -0.29%
                                    -0.55%
                                    -0.53%
                                    -0.65%

Cars > 3106 lbs
                                       -- 
                                     0.42%
                                     0.65%
                                     0.65%
                                    -0.16%
                                    -0.51%
                                    -1.12%

LTs < 4594 lbs
                                       -- 
                                    -0.80%
                                    -1.46%
                                    -1.11%
                                    -0.97%
                                    -0.96%
                                    -1.03%

LTs > 4594 lbs
                                       -- 
                                    -1.17%
                                    -1.15%
                                    -1.01%
                                    -1.11%
                                    -1.56%
                                    -1.59%

CUV/minivan
                                       -- 
                                    -0.96%
                                    -1.34%
                                    -1.35%
                                    -1.02%
                                    -1.42%
                                    -1.53%
Footprint
reduction
Cars
                                       -- 
                                     0.20%
                                    -0.45%
                                    -0.48%
                                     0.57%
                                     0.95%
                                     1.25%

LTs
                                       -- 
                                    -1.81%
                                    -1.57%
                                    -1.84%
                                    -1.63%
                                    -1.46%
                                    -1.37%

CUV/minivan
                                       -- 
                                     1.64%
                                     1.65%
                                     1.60%
                                     1.49%
                                     2.41%
                                     2.57%
Estimates that are statistically significant at the 95% level are shown in red.
* DRI estimates using decimated data for 10 states.  Estimates for track width and wheelbase reductions in cars and light trucks are the weighted average DRI estimates by crash partner weight based on the number of fatalities.

Table 7 compares the DRI and LBNL 2-stage estimates on the effect of mass or footprint reduction on crash frequency (crashes per VMT).  LBNL model 1 predicts results similar to those for DRI only for mass reduction in heavier-than-average light trucks.  LBNL model 1 predicts smaller increases in crash frequency per VMT than DRI from mass reduction in lighter-than-average cars and from footprint reduction in light trucks, while predicting larger increases in crash frequency than DRI from mass reduction in lighter-than-average light trucks and CUVs/minivans, and especially from footprint reduction in cars.  

LBNL model 2 shows that the estimates for crash frequency from mass or footprint reduction in light trucks are particularly sensitive to the vehicles that are included in the decimation sample.  As shown in model 3, adding the three additional states increases the estimated effect of mass reduction on crash frequency in heavier-than-average cars to a statistically-significant 0.75%, but slightly reduces the increase in crash frequency from mass reduction in lighter-than-average light trucks and CUVs/minivans, and substantially reduces the increase in crash frequency from footprint reduction in cars.

LBNL model 4, which uses all of the 13-state crash data, has little effect on the estimates on crash frequency from mass reduction in cars, lighter-than-average light trucks, and CUVs/minivans, but substantially increases the estimate of crash frequency from mass reduction in heavier-than-average light trucks, and decreases the estimated increase in crash frequency from footprint reduction in cars and light trucks.  Model 4 estimates a statistically-significant, but small, decrease in crash frequency from footprint reduction in CUVs/minivans.

LBNL model 5 estimates larger increases in crash frequency from mass reduction, particularly for heavier-than-average cars (from 0.77% to 1.41%), but smaller increases in crash frequency from footprint reduction in cars and light trucks, and a larger decrease in crash frequency from footprint reduction in CUVs/minivans.

Table 7. DRI 2-stage and alternate LBNL 2-stage estimates of the effect of mass or footprint reduction on U.S. crash frequency per VMT (crash avoidance)
Variable
Case vehicle type
A. NHTSA 1-stage estimate
(crashes per VMT)
B. DRI 2-stage estimate (crashes per VMT)
                     C. Alternate LBNL 2-stage estimates 
                              (crashes  per VMT)




1. 10 states, 
decimated crash data
2. 10 states, alternate decimated crash data
3.13 states, 
decimated crash data
4. 13 states, 
all crash data 
5. 13 states, all crash data, duplicated data, where MY matches
Mass
reduction
Cars < 3106 lbs
                                       -- 
                                     2.10%
                                     1.83%
                                     1.86%
                                     1.95%
                                     1.84%
                                     1.96%

Cars > 3106 lbs
                                       -- 
                                     0.16%
                                    -0.10%
                                    -0.05%
                                     0.75%
                                     0.77%
                                     1.41%

LTs < 4594 lbs
                                       -- 
                                     1.41%
                                     1.81%
                                     1.50%
                                     1.30%
                                     1.29%
                                     1.41%

LTs > 4594 lbs
                                       -- 
                                     0.83%
                                     0.76%
                                     0.67%
                                     0.71%
                                     1.04%
                                     1.08%

CUV/minivan
                                       -- 
                                     0.52%
                                     0.86%
                                     0.83%
                                     0.62%
                                     0.80%
                                     0.89%
Footprint
reduction
Cars
                                       -- 
                                     1.20%
                                     2.26%
                                     2.25%
                                     1.27%
                                     1.08%
                                     0.81%

LTs
                                       -- 
                                     1.59%
                                     1.28%
                                     1.45%
                                     1.35%
                                     1.20%
                                     1.09%

CUV/minivan
                                       -- 
                                     0.31%
                                     0.15%
                                     0.29%
                                     0.25%
                                    -0.44%
                                    -0.58%
Estimates that are statistically significant at the 95% level are shown in red.
* DRI estimates using decimated data for 10 states.  Estimates for track width and wheelbase reductions in cars and light trucks are the weighted average DRI estimates by crash partner weight based on the number of fatalities.

Table 8 compares the DRI and LBNL 2-stage estimates with the NHTSA 1-stage estimates on the effect of mass or footprint reduction on U.S. societal fatality risk per VMT.  LBNL model 1 predicts results more similar to NHTSA's results than DRI's results for mass reduction in heavier-than-average cars, and footprint reduction in cars and CUVs/minivans.  However, DRI's 2-stage results for fatality risk per VMT remain more similar to NHTSA's 1-stage results than LBNL's 2-stage results for mass reduction in lighter-than-average cars, light trucks, and CUVs/minivans, and for footprint reduction in light trucks.  LBNL model 2 improves the agreement with NHTSA's 1-stage results for mass reduction in lighter-than-average cars and heavier-than-average light trucks.  LBNL model 3 substantially reduces the estimated effect on fatality risk per VMT from mass reduction in lighter-than-average cars (to 1.40%) and from footprint reduction in CUV/minivans (to 1.74%).  

Using all crash data reduces the estimated detrimental effect of mass reduction, while increasing the estimated detrimental effect of footprint reduction, on fatality risk per VMT for all vehicle types, as shown in LBNL model 4.  LBNL model 5 estimates very similar effects of mass or footprint reduction on U.S. societal fatality risk per VMT as LBNL model 4.

Table 8. NHTSA 1-stage, DRI 2-stage, and alternate LBNL 2-stage estimates of the effect of mass or footprint reduction on U.S. societal fatality risk per VMT
Variable
Case vehicle type
A. NHTSA 1-stage estimate
(fatalities per VMT)
B. DRI 2-stage estimate (fatalities per VMT)
           C. Alternate LBNL 2-stage estimates (fatalities per VMT)




1. 10 states, 
decimated crash data
2. 10 states, alternate decimated crash data
3.13 states, 
decimated crash data
4. 13 states, 
all crash data 
5. 13 states, all crash data, duplicated data, where MY matches
Mass
reduction
Cars < 3106 lbs
                                     1.56%
                                     1.58%
                                     1.48%
                                     1.57%
                                     1.40%
                                     1.31%
                                     1.30%

Cars > 3106 lbs
                                     0.52%
                                     0.58%
                                     0.55%
                                     0.59%
                                     0.59%
                                     0.27%
                                     0.29%

LTs < 4594 lbs
                                     0.52%
                                     0.61%
                                     0.36%
                                     0.39%
                                     0.33%
                                     0.33%
                                     0.38%

LTs > 4594 lbs
                                    -0.34%
                                    -0.34%
                                    -0.39%
                                    -0.34%
                                    -0.40%
                                    -0.52%
                                    -0.51%

CUV/minivan
                                    -0.37%
                                    -0.45%
                                    -0.48%
                                    -0.52%
                                    -0.40%
                                    -0.62%
                                    -0.64%
Footprint
reduction
Cars
                                     1.89%
                                     1.40%
                                     1.80%
                                     1.78%
                                     1.84%
                                     2.03%
                                     2.06%

LTs
                                    -0.07%
                                    -0.23%
                                    -0.29%
                                    -0.38%
                                    -0.28%
                                    -0.25%
                                    -0.28%

CUV/minivan
                                     1.73%
                                     1.96%
                                     1.80%
                                     1.89%
                                     1.74%
                                     1.96%
                                     1.99%
Estimates that are statistically significant at the 95% level are shown in red.
* DRI estimates using decimated data for 10 states.  Estimates for track width and wheelbase reductions in cars and light trucks are the weighted average DRI estimates by crash partner weight based on the number of fatalities.

4. Comparison of results in DRI's Supplemental Report

In its 2012 Supplemental report DRI points out that replacing footprint with two variables, wheelbase and track width, reduces the maximum VIF of the regression models from 6.2 for cars, 10.9 for light trucks, and 8.7 for CUVs/minivans to 5.6 for cars, 6.6 for light trucks, and 7.2 for CUVs/minivans (Tables 2 and 1).  Although DRI argues that replacing footprint with wheelbase and track width reduces the multi-collinearity in the regression model, the maximum VIF is still greater than 5.  

DRI argued that using non-culpable vehicles in two-vehicle crashes as a proxy for all vehicles travelling on road may understate the exposure or VMT of vehicle/driver combinations that could have avoided a two-vehicle crash.  DRI proposed using stopped vehicles struck by another vehicle, rather than the vehicle determined not to be at fault, as a proxy for the distribution of vehicle/driver combinations on the road to be used for induced exposure.  While this proposal makes sense, it must be recognized that using stopped rather than non-culpable vehicles dramatically reduces the number of vehicles in the police-reported crash data available for the induced exposure data: there are 2,242,871 non-culpable vehicles in the NHTSA dataset, while there are only 610,689 (73% fewer) stopped vehicles in the alternate dataset NHTSA developed on DRI's recommendation.

As shown in Table 9, there are slightly smaller fractions of crashes at night, in rural counties, on high speed roads, and with male, young, or old drivers in stopped vehicles than in non-culpable vehicles.  This suggests that stopped vehicles are less influenced by these risky crash or driver characteristics than non-culpable vehicles.  Note that there are much larger fractions of vehicles characterized by these risk factors in the entire database of police-reported crashes than in the two subsets used for the induced exposure.  However, there are slightly higher fractions of crashes involving risky sporty or AWD cars using stopped rather than non-culpable vehicles.  On balance, stopped vehicles, and their drivers, are slightly less risky than non-culpable vehicles/drivers, and therefore may better represent the actual population of on-road vehicles.  However, using stopped rather than non-culpable vehicles substantially reduces the sample of vehicles available for the induced exposure dataset. 

Table 9. Crash, driver, and vehicle characteristics of non-culpable and stopped vehicles used for induced exposure
Variable
      Vehicles involved in two-vehicle crashes used for induced exposure
                            Vehicles in all crashes

                                 Non-culpable
                                    Stopped

NITE

                                     16.1%
                                     13.5%
                                     21.7%
RURAL

                                     24.0%
                                     22.6%
                                     26.6%
SPDLIM55

                                     17.0%
                                     12.4%
                                     24.1%
DRVMALE

                                     46.5%
                                     45.1%
                                     55.4%
DRVAGE
14 to 30
                                     30.3%
                                     27.2%
                                     37.0%

30 to 50
                                     42.8%
                                     45.9%
                                     40.7%

50 to 70
                                     22.6%
                                     23.4%
                                     21.1%

70 to 96
                                     4.3%
                                     3.4%
                                     5.2%
VEHTYPE
2-dr car
                                     7.8%
                                     7.5%
                                     8.2%

4-dr car
                                     43.0%
                                     39.9%
                                     42.9%

Sporty car
                                     1.4%
                                     1.6%
                                     1.5%

Police car
                                     0.8%
                                     0.7%
                                     1.1%

AWD car
                                     1.4%
                                     2.0%
                                     1.3%

Sm pickup
                                     10.1%
                                     10.2%
                                     11.0%

Lg pickup
                                     2.5%
                                     2.3%
                                     3.1%

SUV
                                     15.9%
                                     17.5%
                                     15.3%

CUV
                                     8.4%
                                     9.3%
                                     7.1%

Minivan
                                     6.8%
                                     6.8%
                                     6.1%

Full van
                                     2.0%
                                     2.3%
                                     2.5%

Table 10 shows the sensitivity of the LBNL estimates to the combination of these two changes suggested by DRI, replacing footprint with wheelbase and track width, and using stopped rather than non-culpable vehicles as the basis for induced exposure.  The table compares NHTSA's 1-stage fatality risk per VMT estimates with the DRI and LBNL 2-stage estimates for fatality risk per VMT, as well as for fatality risk per crash and crash frequency per VMT.  The LBNL estimates are from model 5, which uses all crash data from 13 states (including an internal control variable for each state except Florida), as well as duplicate data for four state/CY combinations with missing data, while excluding vehicles where the model year reported in the state crash data did not match the decoded VIN; this dataset most closely resembles the methodology NHTSA used in its analyses.

Comparing columns A, D, and G, the three estimates for fatality risk per VMT, the DRI estimates more closely match the NHTSA estimates for mass reduction in cars and CUVs/minivans, track width reduction in CUVs/minivans, and wheelbase reduction in cars; all of these estimates are small, and none are statistically-significant.  On the other hand, the LBNL estimates more closely match the NHTSA estimates for mass reduction in light trucks, track width reduction in cars and light trucks, and wheelbase reduction in light trucks and CUVs/minivans; five of these six estimates are statistically-significant.

In terms of fatalities per crash (comparing columns B and E), LBNL estimates a more beneficial effect than DRI from mass reduction in cars, heavier-than-average light trucks, and CUVs/minivans; from track width reduction in light trucks; and from wheelbase reduction in CUVs/minivans.  In terms of crash frequency per VMT (comparing columns C and F), LBNL estimates a more beneficial effect than DRI from mass reduction only in lighter-than-average light trucks, from track width reduction only in CUVs/minivans, but from wheelbase reduction in all three types of vehicles.  Note that LBNL estimates a fairly large (1.37%), statistically-significant reduction in crash frequency per VMT from track width reduction in CUVs/minivans.

Table 10.  Comparison of DRI and LBNL estimated effect of mass, track width, or wheelbase reduction on U.S. societal fatality risk per crash, crash frequency per VMT, and fatality risk per VMT
Variable
Case vehicle type
A. NHTSA 1-stage 
(fatalities  per VMT)
                             DRI 2-stage estimate*
LBNL 2-stage estimate**



B. Crashworthiness/ compatibility 
(fatalities per crash)
C. Crash avoidance 
(crashes per VMT)
D. Combined 
(fatalities per VMT)
E. Crashworthiness/ compatibility 
(fatalities per crash)
F. Crash avoidance 
(crashes per VMT)
G. Combined 
(fatalities per VMT)
Mass
reduction
Cars < 3106 lbs
                                     0.26%
                                    -1.05%
                                     1.42%
                                     0.36%
                                    -1.26%
                                     1.71%
                                     0.45%

Cars > 3106 lbs
                                    -0.90%
                                    -0.36%
                                    -0.12%
                                    -0.48%
                                    -2.19%
                                     1.87%
                                    -0.32%

LTs < 4594 lbs
                                    -0.10%
                                    -0.70%
                                     0.75%
                                     0.06%
                                    -0.54%
                                     0.42%
                                    -0.12%

LTs > 4594 lbs
                                    -0.97%
                                    -1.34%
                                     0.50%
                                    -0.84%
                                    -1.68%
                                     0.83%
                                    -0.85%

CUV/minivan
                                    -0.14%
                                    -0.61%
                                     0.39%
                                    -0.22%
                                    -1.39%
                                     0.92%
                                    -0.47%
Track width
reduction
Cars
                                     6.04%
                                     1.34%
                                     1.03%
                                     2.37%
                                     3.66%
                                     1.11%
                                     4.78%

LTs
                                     0.90%
                                    -0.82%
                                     1.23%
                                     0.41%
                                    -2.14%
                                     2.81%
                                     0.68%

CUV/minivan
                                    -0.55%
                                    -0.44%
                                     0.13%
                                    -0.31%
                                     0.33%
                                    -1.37%
                                    -1.04%
Wheelbase reduction
Cars
                                     0.38%
                                    -0.43%
                                     0.81%
                                     0.38%
                                     0.30%
                                     0.18%
                                     0.47%

LTs
                                    -0.09%
                                    -1.12%
                                     0.77%
                                    -0.35%
                                    -0.44%
                                     0.21%
                                    -0.23%

CUV/minivan
                                     1.45%
                                     2.20%
                                     0.45%
                                     2.65%
                                     1.82%
                                     0.04%
                                     1.86%
Estimates that are statistically significant at the 95% level are shown in red.
* DRI estimates using decimated data for 10 states.  Estimates for track width and wheelbase reductions in cars and light trucks are the weighted average DRI estimates by crash partner weight based on the number of fatalities.
** LBNL estimates using all non-fatal crash data for 13 states (with 12 internal control variables), duplicated data for missing state/CY combinations, and where the MY reported in state crash data matches the decoded VIN. 



                                       
                                       
                                       
                                       
                                       
                                       
                                       
                                       
                                       
                                       
                                       
                                       
                                       
                                       
                                       
           APPENDIX A. COMPARISON OF DRI AND LBNL TWO-STAGE RESULTS


Table A-1. DRI and LBNL 2-stage estimated effect of mass or footprint reduction on US fatality risk per crash, crash frequency per VMT, and fatality risk per VMT
Variable
Case vehicle type
A. NHTSA 1-stage 
(fatalities  per VMT)
                             DRI 2-stage estimate*
                            LBNL 2-stage estimates



                                       
                                1. 10 states, 
                             decimated crash data
                 2. 10 states, alternate decimated crash data



B. Crashworthiness/ compatibility 
(fatalities per crash)
C. Crash avoidance 
(crashes per VMT)
D. Combined 
(fatalities per VMT)
E. Crashworthiness/ compatibility 
(fatalities per crash)
F. Crash avoidance 
(crashes per VMT)
G. Combined 
(fatalities per VMT)
H. Crashworthiness/ compatibility 
(fatalities per crash)
I. Crash avoidance 
(crashes per VMT)
J. Combined 
(fatalities per VMT)
Mass
reduction
Cars < 3106 lbs
                                     1.56%
                                    -0.51%
                                     2.10%
                                     1.58%
                                    -0.35%
                                     1.83%
                                     1.48%
                                    -0.29%
                                     1.86%
                                     1.57%

Cars > 3106 lbs
                                     0.52%
                                     0.42%
                                     0.16%
                                     0.58%
                                     0.65%
                                    -0.10%
                                     0.55%
                                     0.65%
                                    -0.05%
                                     0.59%

LTs < 4594 lbs
                                     0.52%
                                    -0.80%
                                     1.41%
                                     0.61%
                                    -1.46%
                                     1.81%
                                     0.36%
                                    -1.11%
                                     1.50%
                                     0.39%

LTs > 4594 lbs
                                    -0.34%
                                    -1.17%
                                     0.83%
                                    -0.34%
                                    -1.15%
                                     0.76%
                                    -0.39%
                                    -1.01%
                                     0.67%
                                    -0.34%

CUV/minivan
                                    -0.37%
                                    -0.96%
                                     0.52%
                                    -0.45%
                                    -1.34%
                                     0.86%
                                    -0.48%
                                    -1.35%
                                     0.83%
                                    -0.52%
Footprint
reduction
Cars
                                     1.89%
                                     0.20%
                                     1.20%
                                     1.40%
                                    -0.45%
                                     2.26%
                                     1.80%
                                    -0.48%
                                     2.25%
                                     1.78%

LTs
                                    -0.07%
                                    -1.81%
                                     1.59%
                                    -0.23%
                                    -1.57%
                                     1.28%
                                    -0.29%
                                    -1.84%
                                     1.45%
                                    -0.38%

CUV/minivan
                                     1.73%
                                     1.64%
                                     0.31%
                                     1.96%
                                     1.65%
                                     0.15%
                                     1.80%
                                     1.60%
                                     0.29%
                                     1.89%
Estimates that are statistically significant at the 95% level are shown in red.
* DRI estimates using decimated data for 10 states.  Estimates for track width and wheelbase reductions in cars and light trucks are the weighted average DRI estimates by crash partner weight based on the number of fatalities.

Table A-2. LBNL 2-stage estimated effect of mass or footprint reduction on US fatality risk per crash, crash frequency per VMT, and fatality risk per VMT, using 13 NHTSA states
Variable
Case vehicle type
A. NHTSA 1-stage 
(fatalities  per VMT)
                            LBNL 2-stage estimates



                                3. 13 states, 
                             decimated crash data
                                4. 13 states, 
                                all crash data
        5. 13 states, all crash data, duplicated data, where MY matches



B. Crashworthiness/ compatibility 
(fatalities per crash)
C. Crash avoidance 
(crashes per VMT)
D. Combined 
(fatalities per VMT)
E. Crashworthiness/ compatibility 
(fatalities per crash)
F. Crash avoidance 
(crashes per VMT)
G. Combined 
(fatalities per VMT)
H. Crashworthiness/ compatibility 
(fatalities per crash)
I. Crash avoidance 
(crashes per VMT)
J. Combined 
(fatalities per VMT)
Mass
reduction
Cars < 3106 lbs
                                     1.56%
                                    -0.55%
                                     1.95%
                                     1.40%
                                    -0.53%
                                     1.84%
                                     1.31%
                                    -0.65%
                                     1.96%
                                     1.30%

Cars > 3106 lbs
                                     0.52%
                                    -0.16%
                                     0.75%
                                     0.59%
                                    -0.51%
                                     0.77%
                                     0.27%
                                    -1.12%
                                     1.41%
                                     0.29%

LTs < 4594 lbs
                                     0.52%
                                    -0.97%
                                     1.30%
                                     0.33%
                                    -0.96%
                                     1.29%
                                     0.33%
                                    -1.03%
                                     1.41%
                                     0.38%

LTs > 4594 lbs
                                    -0.34%
                                    -1.11%
                                     0.71%
                                    -0.40%
                                    -1.56%
                                     1.04%
                                    -0.52%
                                    -1.59%
                                     1.08%
                                    -0.51%

CUV/minivan
                                    -0.37%
                                    -1.02%
                                     0.62%
                                    -0.40%
                                    -1.42%
                                     0.80%
                                    -0.62%
                                    -1.53%
                                     0.89%
                                    -0.64%
Footprint
reduction
Cars
                                     1.89%
                                     0.57%
                                     1.27%
                                     1.84%
                                     0.95%
                                     1.08%
                                     2.03%
                                     1.25%
                                     0.81%
                                     2.06%

LTs
                                    -0.07%
                                    -1.63%
                                     1.35%
                                    -0.28%
                                    -1.46%
                                     1.20%
                                    -0.25%
                                    -1.37%
                                     1.09%
                                    -0.28%

CUV/minivan
                                     1.73%
                                     1.49%
                                     0.25%
                                     1.74%
                                     2.41%
                                    -0.44%
                                     1.96%
                                     2.57%
                                    -0.58%
                                     1.99%
Estimates that are statistically significant at the 95% level are shown in red.
* DRI estimates using decimated data for 10 states.  Estimates for track width and wheelbase reductions in cars and light trucks are the weighted average DRI estimates by crash partner weight based on the number of fatalities.
