Document ID: EPA-HQ-OAR-2011-0135-0665
Agency: epa
Document Type: Supporting & Related Material
Title: 
Posted Date: 2013-04-18T04:00Z

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  L.3
                                       
                                       
                         Model Fitting Information for
                             Formaldehyde (Bag 1)

This appendix summarizes model fitting for Formaldehyde (Bag 1).  Model-fitting techniques and approaches are described in Section 8.7.  Features of the data and modeling for this compound are listed below.

Fuel-parameter matrix:	FULL
No. measurements:	956
No. vehicles:		15
No. censored values:	0
Modeling approach:	MIXED MODEL

Models fit for Formaldehyde (Bag 1).
Model Term
                                   Notation
                                     Model

                                       
                                  Full Model
FM4
FM5
FM6
FM7
Linear Effects
etOH
Ze
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
Arom
Za
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
RVP
Zr
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
T50
Z5
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
T90
Z9
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
etOH x etOH
ZZee
                                      ●
                                      ●
                                      ●
                                      x
                                       
                                       
T50 x T50
ZZ55
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
etOH x Arom
ZZea
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
etOH x RVP
ZZer
                                      ●
                                      x
                                       
                                       
                                       
                                       
etOH x T50
ZZe5
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
etOH x T90
ZZe9
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
Arom x RVP
ZZar
                                      ●
                                      x
                                       
                                       
                                       
                                       
Arom x T50
ZZa5
                                      ●
                                      x
                                       
                                       
                                       
                                       
Arom x T90
ZZa9
                                      ●
                                      ●
                                      x
                                       
                                       
                                       
T90 x T90
ZZ99
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
                                       
T50 x T90
ZZ59
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
RVP x T90
ZZr9
                                      ●
                                      x
                                       
                                       
                                       
                                       

Fitting history for Bag-1 Formaldehyde  -  with "FM7" selected as the reduced 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
                                                                             17
                                                                       -102.866
                                                                        -48.705

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
FM4
                                                                             13
                                                                       -101.651
                                                                        -58.322

                                                                          1.215
                                                                              4
                                                                          0.876
                                                                               
                                                                               
                                                                               
                                                                               
FM5
                                                                             12
                                                                       -100.336
                                                                        -59.715

                                                                          2.530
                                                                              5
                                                                          0.772
                                                                               
                                                                          1.315
                                                                              1
                                                                          0.252
FM6
                                                                             11
                                                                        -99.040
                                                                        -61.127

                                                                          3.826
                                                                              6
                                                                          0.700
                                                                               
                                                                          1.296
                                                                              1
                                                                          0.255
FM7[2]
                                                                             10
                                                                        -95.848
                                                                        -60.643

                                                                          7.018
                                                                              7
                                                                          0.427
                                                                               
                                                                          3.192
                                                                              1
                                                                          0.074
Linear Effects
                                                                              5
                                                                        -13.166
                                                                          8.498

                                                                         89.700
                                                                             12
                                                                       0.000000
                                                                               
                                                                         82.682
                                                                              5
                                                                       0.000000
[1] A lower value indicates a better fit.
[2] Selected as "best fit" with respect to the 17-term full model.
Note that based on the history, FM6 is actually the "best fit," however, we have retained FM7 due to the decision to exclude the T90xT90 term from final model fitting. See Section 7.2.1.

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

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

                             Best-Fit Model (FM7)

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

Estimate
Std.Err.
d.f.
t-value
Pr>t
Intercept
                                                                               
                                                                        -5.9771
                                                                         0.1498
                                                                             15
                                                                          -39.9
                                                                       0.000000

                                                                        -5.9771
                                                                         0.1498
                                                                             15
                                                                          -39.9
                                                                       0.000000
Ze
                                                                               
                                                                         0.2279
                                                                        0.01234
                                                                            898
                                                                           18.5
                                                                       0.000000

                                                                         0.2299
                                                                       0.009640
                                                                            898
                                                                           23.8
                                                                       0.000000
Za
                                                                               
                                                                        0.03528
                                                                       0.008841
                                                                            898
                                                                           3.99
                                                                       0.000071

                                                                        0.02822
                                                                       0.007979
                                                                            898
                                                                           3.54
                                                                        0.00043
Zr
                                                                               
                                                                       -0.05202
                                                                        0.01234
                                                                            898
                                                                          -4.21
                                                                       0.000028

                                                                       -0.04718
                                                                       0.008457
                                                                            898
                                                                          -5.58
                                                                       0.000000
Z5
                                                                               
                                                                         0.1577
                                                                        0.01738
                                                                            898
                                                                           9.07
                                                                       0.000000

                                                                         0.1672
                                                                        0.01001
                                                                            898
                                                                           16.7
                                                                       0.000000
Z9
                                                                               
                                                                         0.1357
                                                                        0.01064
                                                                            898
                                                                           12.7
                                                                       0.000000

                                                                         0.1302
                                                                       0.007360
                                                                            898
                                                                           17.7
                                                                       0.000000
ZZee
                                                                               
                                                                       -0.01498
                                                                        0.01475
                                                                            898
                                                                          -1.02
                                                                           0.31

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
ZZ55
                                                                               
                                                                        0.05026
                                                                        0.01251
                                                                            898
                                                                           4.02
                                                                       0.000064

                                                                        0.05262
                                                                       0.008341
                                                                            898
                                                                           6.31
                                                                       0.000000
ZZea
                                                                               
                                                                        0.02017
                                                                        0.01241
                                                                            898
                                                                           1.63
                                                                           0.10

                                                                        0.01651
                                                                       0.007340
                                                                            898
                                                                           2.25
                                                                          0.025
ZZer
                                                                               
                                                                       0.004100
                                                                       0.008366
                                                                            898
                                                                          0.490
                                                                           0.62

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
ZZe5
                                                                               
                                                                       -0.03686
                                                                        0.01594
                                                                            898
                                                                          -2.31
                                                                          0.021

                                                                       -0.01627
                                                                       0.008177
                                                                            898
                                                                          -1.99
                                                                          0.047
ZZe9
                                                                               
                                                                        0.02181
                                                                        0.01023
                                                                            898
                                                                           2.13
                                                                          0.033

                                                                        0.02004
                                                                       0.008838
                                                                            898
                                                                           2.27
                                                                          0.024

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
ZZar
                                                                               
                                                                       0.007384
                                                                        0.01535
                                                                            898
                                                                          0.481
                                                                           0.63

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
ZZa5
                                                                               
                                                                      -0.006739
                                                                        0.01645
                                                                            898
                                                                          -0.41
                                                                           0.68

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
ZZa9
                                                                               
                                                                       -0.01036
                                                                       0.008437
                                                                            898
                                                                          -1.23
                                                                           0.22

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
ZZ99
                                                                               
                                                                        0.02104
                                                                        0.01435
                                                                            898
                                                                           1.47
                                                                           0.14

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
ZZ59
                                                                               
                                                                        0.03974
                                                                        0.01080
                                                                            898
                                                                           3.68
                                                                        0.00025

                                                                        0.03489
                                                                       0.009322
                                                                            898
                                                                           3.74
                                                                        0.00019
ZZr9
                                                                               
                                                                      -0.003140
                                                                       0.009498
                                                                            898
                                                                         -0.331
                                                                           0.74

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                         0.3360
                                                                               
                                                                               
                                                                               
                                                                               

                                                                         0.3358
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                         0.1395
                                                                               
                                                                               
                                                                               
                                                                               

                                                                         0.1406