Document ID: EPA-HQ-OAR-2011-0135-0595
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
                                       
                       Analysis of Data from EPA Phase 3
                                       
                                       
                                (EPAct/V2/E-89)

                                 Appendix  N.3
                                       
                                       
                         Model Fitting Information for
                                Ethanol (Bag 1)

This appendix summarizes model fitting for Bag-1 Ethanol.  Model-fitting techniques and approaches summarized in Section 8.7.  Features of the data and modeling for this compound are listed below.
Fuel-parameter matrix:	FULL
Media contamination:	YES
No. measurements:	913
No. censored values:	193
Modeling approach:	TOBIT REGRESSION
Estimated Dependent Variable model:	YES

Models fit for Ethanol, Bag 1 (all models include an intercept term) 
Model Term
                                   Notation
                                     Model

                                       
                                     Full
FM6
FM9
FM10
FM11
                                     etOH
Ze
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                     Arom
Za
                                      ●
                                      ●
                                      x
                                       
                                       
                                      RVP
Zr
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      T50
Z5
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      T90
Z9
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                 etOH x etOH
ZZee
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                  T50 x T50
ZZ55
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                 etOH x Arom
ZZea
                                      ●
                                      x
                                       
                                       
                                       
                                  etOH x T50
ZZe5
                                      ●
                                      x
                                       
                                       
                                       
                                  etOH x T90
ZZe9
                                      ●
                                      x
                                       
                                       
                                       
                                  etOH x RVP
ZZer
                                      ●
                                      x
                                       
                                       
                                       
                                  Arom x T50
ZZa5
                                      ●
                                      ●
                                      x
                                       
                                       
                                  Arom x T90
ZZa9
                                      ●
                                      x
                                       
                                       
                                       
                                  T90 x T90
ZZ99
                                      ●
                                      ●
                                      ●
                                      x
                                       
                                  T50 x T90
ZZ59
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
                                  Arom x RVP
ZZar
                                      ●
                                      ●
                                      x
                                       
                                       
                                  RVP x T90
ZZr9
                                      ●
                                      x
                                       
                                       
                                       

 Model Fitting History for Ethanol, Bag 1 (FM11 selected as best-fit model).
                                Fit Parameters

                             Test with respect to
                                     Full

                             Test with respect to
                                Previous Model
Model
                                                                              p
-2lnL
BIC[1]

                                                                        Dev.[1]
                                                                              d
                                                                    Pr>χ[2]
                                                                               
                                                                           Dev.
                                                                              d
                                                                    Pr>χ[2]
Full
                                                                             18
632.42
750.84

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
FM6
                                                                             12
633.33
712.28

                                                                         0.9125
                                                                              6
                                                                           0.99
                                                                               
                                                                               
                                                                               
                                                                               
FM9
                                                                              9
634.97
694.18

                                                                         2.5494
                                                                              9
                                                                           0.98
                                                                               
                                                                         1.6369
                                                                              3
                                                                           0.65
FM10
                                                                              8
635.10
687.74

                                                                         2.6863
                                                                             10
                                                                           0.99
                                                                               
                                                                         0.1369
                                                                              1
                                                                           0.71
FM11
                                                                              7
637.88
683.93

                                                                         5.4581
                                                                             11
                                                                           0.91
                                                                               
                                                                         2.7719
                                                                              1
                                                                          0.095
[1] A lower value indicates a better fit.

[1] The deviation is the difference in
the -2loglik statistics for the 
nested and reference models,
respectively, per Equation 14.

 
Coefficients and Tests of Effect for the Full and Best-Fit Models  -  Ethanol (Bag 1).
Effect
                                       
                                  Full Model

                             Best-Fit Model (FM11)

Estimate
Std.Err.
d.f.
t-value
Pr>t

                                                                       Estimate
Std.Err.
d.f.
t-value
Pr>t
Intercept[1]
                                                                               
                                                                               
                                                                               
                                                                             15
                                                                               
                                                                               

                                                                        -4.9081
                                                                               
                                                                               
                                                                               
                                                                               
Ze
                                                                               
                                                                         1.4759
                                                                        0.07240
                                                                             15
                                                                          20.38
                                                                    <0.00001

                                                                         1.4643
                                                                        0.07115
                                                                             15
                                                                          20.56
                                                                    <0.00001
Za
                                                                               
                                                                        -0.0067
                                                                        0.04327
                                                                             15
                                                                          -0.16
                                                                           0.88

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
Zr
                                                                               
                                                                       -0.05004
                                                                        0.04316
                                                                             15
                                                                          -1.16
                                                                           0.26

                                                                       -0.05990
                                                                        0.02940
                                                                             15
                                                                          -2.06
                                                                          0.057
Z5
                                                                               
                                                                         0.1050
                                                                        0.03806
                                                                             15
                                                                           2.76
                                                                          0.015

                                                                        0.07188
                                                                        0.02964
                                                                             15
                                                                           2.37
                                                                          0.032
Z9
                                                                               
                                                                        -0.1261
                                                                        0.03701
                                                                             15
                                                                          -3.47
                                                                         0.0034

                                                                       -0.09990
                                                                        0.03574
                                                                             15
                                                                          -2.78
                                                                          0.014
ZZee
                                                                               
                                                                        -0.4787
                                                                        0.06014
                                                                             15
                                                                          -7.96
                                                                    <0.00001

                                                                        -0.4967
                                                                        0.05229
                                                                             15
                                                                          -9.51
                                                                    <0.00001
ZZ55
                                                                               
                                                                         0.1261
                                                                        0.05018
                                                                             15
                                                                           2.51
                                                                          0.024

                                                                         0.1121
                                                                        0.03826
                                                                             15
                                                                           2.90
                                                                          0.011
ZZea
                                                                               
                                                                      -0.005952
                                                                        0.03881
                                                                             15
                                                                          -0.15
                                                                           0.88

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
ZZe5
                                                                               
                                                                        0.02820
                                                                        0.05277
                                                                             15
                                                                           0.54
                                                                           0.60

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
ZZe9
                                                                               
                                                                      0.0008509
                                                                        0.06491
                                                                             15
                                                                         0.0090
                                                                           0.99

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
ZZer
                                                                               
                                                                        0.03237
                                                                        0.05103
                                                                             15
                                                                           0.64
                                                                           0.53

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
ZZa5
                                                                               
                                                                        0.03318
                                                                        0.03212
                                                                             15
                                                                           1.04
                                                                           0.32

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
ZZa9
                                                                               
                                                                       -0.01143
                                                                        0.03461
                                                                             15
                                                                          -0.33
                                                                           0.74

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
ZZ99
                                                                               
                                                                        -0.5112
                                                                        0.04523
                                                                             15
                                                                          -1.13
                                                                           0.28

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
ZZ59
                                                                               
                                                                        0.05311
                                                                        0.04341
                                                                             15
                                                                           1.22
                                                                           0.24

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
ZZar
                                                                               
                                                                        0.04136
                                                                        0.02855
                                                                             15
                                                                           1.45
                                                                           0.17

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
ZZr9
                                                                               
                                                                      -0.008676
                                                                        0.04644
                                                                             15
                                                                          -0.20
                                                                           0.85

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
[1]
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               

                                                                         0.1283
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                         0.5697
                                                                               
                                                                               
                                                                               
                                                                               

                                                                        0.05739
                                                                               
                                                                               
                                                                               
                                                                               
[1] Not fit by the model, but manually recalculated from intercepts for individual vehicles.

  Coefficients for Models (FM11) for individual Jackknife replicates used to calculate standard errors for model terms.