Document ID: EPA-HQ-OAR-2011-0135-0576
Agency: epa
Document Type: Supporting & Related Material
Title: 
Posted Date: 2013-04-16T04:00Z

Assessing the Effect of Five Gasoline Properties on Exhaust Emissions from Light-Duty Vehicles certified to Tier-2 Standards
                           (EPAct/V2/E-89: Phase 3)
                                       
                 Part II:  Data Analysis and Model Development
                                        
                                  APPENDIX  E
                            
                            Preliminary Reduced Models

Development of the models presented below is described in Section 5.3 of the report. All models are based on the 16-parameter full model, as shown in Equation 1.  All terms were included at the outset of model fitting, with the exception of T90xT90. Using the notation for standardized predictors, also shown in Equation 2, the model is also expressed in Equation 2. Table E.1 summarizes the model-fitting approaches applied to each bag for each emission.  Table E.2 through E.7 present the coefficients for interim reduced models for THC, NMOG, CH4, CO, NOx and PM, respectively.    

                                                                     Equation 1

                                                                     Equation 2

 Table E.1.  Design and Modeling Parameters for Best-fit models, by Compound and Bag. 
Compound 
                                      Bag
nremoved
Model Type
Selection Method
THC
                                       1
                                       0
                                     Mixed
                                 Minimize BIC

                                       2
                                       0
                                     Mixed
                                 Minimize BIC

                                       3
                                       0
                                     Mixed
                                 Minimize BIC
CO
                                       1
                                       0
                                     Mixed
                                 Minimize BIC

                                       2
                                       0
                                     Mixed
                                 Minimize BIC

                                       3
                                       0
                                     Mixed
                                 Minimize BIC
NOx
                                       1
                                       0
                                     Mixed
                                 Minimize BIC

                                       2
                                       0
                                     Mixed
                                 Minimize BIC

                                       3
                                       0
                                     Tobit
                             Backwards elimination
PM
                                       1
                                       2
                                     Tobit
                             Backwards elimination

                                       2
                                       1
                                     Tobit
                             Backwards elimination

                                       3
                                       1
                                     Tobit
                             Backwards elimination
NMOG
                                       1
                                       0
                                     Mixed
                                 Minimize BIC

                                       2
                                       0
                                     Tobit
                             Backwards elimination

                                       3
                                       0
                                     Tobit
                             Backwards elimination
CH4
                                       1
                                       0
                                     Mixed
                             Backwards elimination

                                       2
                                       0
                                     Mixed
                             Backwards elimination

                                       3
                                       0
                                     Mixed
                             Backwards elimination

Table E.2.   THC:  Reduced Models, starting from 16-term full model.
Model term
Notation
                                                                          Bag 1
                                                                          Bag 2
                                                                          Bag 3
Intercept
Intercept
                                                                        -0.8658
                                                                        -4.9092
                                                                        -4.2300
etOH
Ze
                                                                        0.06793
                                                                        0.06814
                                                                       0.007879
Arom
Za
                                                                        0.08343
                                                                       -0.02281
                                                                       -0.06120
RVP
Zr
                                                                       -0.04669
                                                                               
                                                                       -0.01423
T50
Z5
                                                                         0.1490
                                                                       -0.03953
                                                                        0.03595
T90
Z9
                                                                        0.01435
                                                                        0.07154
                                                                        0.04904
etOH x etOH
ZZee
                                                                        0.04065
                                                                        0.06681
                                                                               
T50 x T50
ZZ55
                                                                        0.07555
                                                                               
                                                                               
etOH x Arom
ZZea
                                                                        0.02297
                                                                        0.03054
                                                                               
etOH x RVP
ZZer
                                                                               
                                                                               
                                                                        0.01666
etOH x T50
ZZe5
                                                                        0.03426
                                                                        0.04028
                                                                       -0.03125
etOH x T90
ZZe9
                                                                        0.04782
                                                                               
                                                                               

                                                                               
                                                                               
                                                                               
Arom x RVP
ZZar
                                                                               
                                                                               
                                                                               
Arom x T50
ZZa5
                                                                               
                                                                        0.03386
                                                                               
Arom x T90
ZZa9
                                                                        0.02264
                                                                               
                                                                               
T50 x T90
ZZ59
                                                                               
                                                                        0.02886
                                                                               
RVP x T90
ZZr9
                                                                               
                                                                               
                                                                               

Table E.3.  NMOG:  Reduced Models, starting from 16-term full model.
Model term
Notation
                                                                          Bag 1
                                                                          Bag 2
                                                                          Bag 3
Intercept
Intercept
                                                                         0.9513
                                                                     -5.5166[1]
                                                                     -5.8449[1]
etOH
Ze
                                                                        0.09272
                                                                         0.0730
                                                                         0.0339
Arom
Za
                                                                         0.1051
                                                                         0.0355
                                                                               
RVP
Zr
                                                                       -0.04834
                                                                        -0.0463
                                                                        -0.0572
T50
Z5
                                                                         0.1541
                                                                         0.0859
                                                                         0.0783
T90
Z9
                                                                        0.01124
                                                                         0.1091
                                                                         0.1467
etOH x etOH
ZZee
                                                                        0.04204
                                                                        -0.0424
                                                                               
T50 x T50
ZZ55
                                                                        0.07866
                                                                         0.0412
                                                                               
etOH x Arom
ZZea
                                                                        0.02171
                                                                         0.0718
                                                                               
etOH x RVP
ZZer
                                                                               
                                                                        -0.0313
                                                                         0.0707
etOH x T50
ZZe5
                                                                        0.03576
                                                                               
                                                                        -0.0728
etOH x T90
ZZe9
                                                                        0.04763
                                                                               
                                                                               

                                                                               
                                                                               
                                                                               
Arom x RVP
ZZar
                                                                        0.02724
                                                                               
                                                                               
Arom x T50
ZZa5
                                                                               
                                                                         0.0738
                                                                               
Arom x T90
ZZa9
                                                                        0.02049
                                                                         0.0327
                                                                               
T50 x T90
ZZ59
                                                                        0.05437
                                                                         0.0293
                                                                               
RVP x T90
ZZr9
                                                                               
                                                                               
                                                                               
                                                                               
[1] Not fit by Tobit model; calculated manually from intercepts for individual vehicles.
Table E.4.  CH4:  Reduced Models, starting from 16-term full model.
Model term
Notation
                                                                          Bag 1
                                                                          Bag 2
                                                                          Bag 3
Intercept
Intercept
                                                                        -3.0068
                                                                        -5.7076
                                                                        -4.5979
etOH
Ze
                                                                        0.08877
                                                                        0.06076
                                                                        0.03187
Arom
Za
                                                                       -0.09816
                                                                       -0.09211
                                                                        -0.1004
RVP
Zr
                                                                       -0.02455
                                                                       -0.02082
                                                                               
T50
Z5
                                                                         0.1059
                                                                        0.04477
                                                                        0.01886
T90
Z9
                                                                       0.008573
                                                                        0.02445
                                                                        0.01856
etOH x etOH
ZZee
                                                                        0.03133
                                                                               
                                                                               
T50 x T50
ZZ55
                                                                        0.05882
                                                                        0.01398
                                                                               
etOH x Arom
ZZea
                                                                        0.03977
                                                                        0.01047
                                                                               
etOH x RVP
ZZer
                                                                               
                                                                               
                                                                               
etOH x T50
ZZe5
                                                                        0.02883
                                                                               
                                                                       -0.02007
etOH x T90
ZZe9
                                                                        0.02655
                                                                               
                                                                               

                                                                               
                                                                               
                                                                               
Arom x RVP
ZZar
                                                                        0.02791
                                                                               
                                                                               
Arom x T50
ZZa5
                                                                        0.02585
                                                                               
                                                                               
Arom x T90
ZZa9
                                                                        0.03072
                                                                               
                                                                               
T50 x T90
ZZ59
                                                                         0.0228
                                                                        0.01374
                                                                               
RVP x T90
ZZr9
                                                                               
                                                                       -0.00992
                                                                               
                                                                               

Table E.5.   CO: Reduced Models, starting from 16-term full model.
Model term
Notation
                                                                          Bag 1
                                                                          Bag 2
                                                                          Bag 3
Intercept
Intercept
                                                                         1.3472
                                                                        -1.3896
                                                                        -1.1409
etOH
Ze
                                                                       -0.06967
                                                                               
                                                                       -0.08154
Arom
Za
                                                                       -0.01156
                                                                        0.09798
                                                                        0.07191
RVP
Zr
                                                                        0.02063
                                                                        0.02838
                                                                        0.02393
T50
Z5
                                                                        0.02159
                                                                        0.02486
                                                                               
T90
Z9
                                                                        -0.1469
                                                                        0.04180
                                                                        0.05781
etOH x etOH
ZZee
                                                                        0.08535
                                                                               
                                                                               
T50 x T50
ZZ55
                                                                        0.07222
                                                                               
                                                                               
etOH x Arom
ZZea
                                                                        0.06244
                                                                               
                                                                               
etOH x RVP
ZZer
                                                                               
                                                                               
                                                                               
etOH x T50
ZZe5
                                                                         0.1117
                                                                               
                                                                               
etOH x T90
ZZe9
                                                                               
                                                                               
                                                                               

                                                                               
                                                                               
                                                                               
Arom x RVP
ZZar
                                                                               
                                                                               
                                                                               
Arom x T50
ZZa5
                                                                               
                                                                               
                                                                               
Arom x T90
ZZa9
                                                                        0.03861
                                                                               
                                                                               
T50 x T90
ZZ59
                                                                               
                                                                        0.02177
                                                                               
RVP x T90
ZZr9
                                                                               
                                                                               
                                                                               
Table E.6.  NOx: Reduced Models, starting from 16-term full model.
Model term
Notation
                                                                          Bag 1
                                                                          Bag 2
                                                                          Bag 3
Intercept
Intercept
                                                                       -3.01636
                                                                        -4.7882
                                                                        -5.2554
etOH
Ze
                                                                        0.03802
                                                                        0.04112
                                                                         0.0884
Arom
Za
                                                                         0.1336
                                                                        0.03534
                                                                         0.0667
RVP
Zr
                                                                       -0.01418
                                                                       -0.01464
                                                                          0.169
T50
Z5
                                                                        0.01026
                                                                               
                                                                        -0.0224
T90
Z9
                                                                        0.02389
                                                                     -0.0004567
                                                                          0.085
etOH x etOH
ZZee
                                                                       -0.05980
                                                                               
                                                                               
T50 x T50
ZZ55
                                                                       -0.05701
                                                                               
                                                                               
etOH x Arom
ZZea
                                                                       -0.03038
                                                                        0.02739
                                                                               
etOH x RVP
ZZer
                                                                               
                                                                               
                                                                               
etOH x T50
ZZe5
                                                                        -0.9774
                                                                               
                                                                         0.0637
etOH x T90
ZZe9
                                                                        0.02544
                                                                               
                                                                               

                                                                               
                                                                               
                                                                               
Arom x RVP
ZZar
                                                                               
                                                                               
                                                                               
Arom x T50
ZZa5
                                                                               
                                                                               
                                                                         0.0894
Arom x T90
ZZa9
                                                                       -0.04769
                                                                               
                                                                               
T50 x T90
ZZ59
                                                                               
                                                                               
                                                                               
RVP x T90
ZZr9
                                                                        0.04562
                                                                       -0.04014
                                                                               

Table E.7.   PM: Reduced models, starting from 16-term full model.
Model term
Notation
                                                                          Bag 1
                                                                          Bag 2
                                                                          Bag 3
                                   Intercept

                                                                               
                                                                               
                                                                               
                                     etOH
Ze
                                                                         0.1640
                                                                         0.1158
                                                                       -0.02120
                                     Arom
Za
                                                                         0.3795
                                                                         0.1988
                                                                        0.01860
                                      RVP
Zr
                                                                               
                                                                               
                                                                        -0.1275
                                      T50
Z5
                                                                        0.06650
                                                                       -0.00370
                                                                       -0.04110
                                      T90
Z9
                                                                         0.2882
                                                                        0.09530
                                                                               
                                 etOH x etOH
ZZee
                                                                               
                                                                               
                                                                               
                                  T50 x T50
ZZ55
                                                                        0.08560
                                                                               
                                                                               
                                 etOH x Arom
ZZea
                                                                               
                                                                               
                                                                        0.08490
                                  etOH x RVP
ZZer
                                                                               
                                                                               
                                                                               
                                  etOH x T50
ZZe5
                                                                               
                                                                               
                                                                       -0.08240
                                  etOH x T90
ZZe9
                                                                               
                                                                               
                                                                               
                                       

                                                                               
                                                                               
                                                                               
                                  Arom x RVP
ZZar
                                                                               
                                                                               
                                                                        -0.1062
                                  Arom x T50
ZZa5
                                                                               
                                                                               
                                                                               
                                  Arom x T90
ZZa9
                                                                               
                                                                               
                                                                               
                                  T50 x T90
ZZ59
                                                                               
                                                                         0.1059
                                                                               
                                  RVP x T90
ZZr9