Document ID: EPA-HQ-OAR-2011-0135-0588
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  P.3
                                       
                                       
                         Model Fitting Information for
                             1,3-Butadiene (Bag 1)

This appendix suFMarizes model fitting for Bag-1 1,3-Butadiene.  Model-fitting techniques and approaches suFMarized in Section 8.7.  Features of the data and modeling for this compound are listed below.
Fuel-parameter matrix:	REDUCED
Media contamination:	NO
No. measurements:	62
No. censored values:	0
Modeling approach:	MIXED MODEL
Estimated Dependent Variable model:	NO

Models fit for 1,3-Butadiene (Bag 1)
Model term
                                   Notation
                                     Model

                                       
                          Full Model (Linear Effects)
FM1[1]
FM2
FM3
Null Model[2]
                                     etOH
Ze
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
                                     Arom
Za
                                      ●
                                      ●
                                      x
                                       
                                       
                                      T50
Z5
                                      ●
                                      ●
                                      ●
                                      x
                                       
                                      T90
Z9
                                      ●
                                      x
                                       
                                       
                                       
[1] Denotes "Full minus 1," etc.
[2] Model fit with intercept only.

 Fitting history for 1,3-Butadiene (Bag 1)  -  with "FM3" selected as best fit model.
                                Fit Parameters

                             Test with respect to
                                   Benchmark

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

                                                                        Dev.[1]
                                                                              d
                                                                    Pr>χ[2]
                                                                               
                                                                           Dev.
                                                                              d
                                                                    Pr>χ[2]
Linear Effects
5
                                                                          21.82
                                                                          33.08

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
FM1
4
                                                                          22.07
                                                                          31.73

                                                                         0.2556
                                                                              1
                                                                           0.61
                                                                               
                                                                               
                                                                               
                                                                               
FM2
3
                                                                          22.61
                                                                          30.66

                                                                         0.7939
                                                                              1
                                                                           0.37
                                                                               
	0.5383
                                                                              1
                                                                           0.46
FM3
2
                                                                          23.66
                                                                          30.10

                                                                         1.8468
                                                                              1
                                                                           0.17
                                                                               
                                                                         1.0529
                                                                              1
                                                                           0.30
Null Model
1
                                                                          39.80
                                                                          44.63

                                                                          17.98
                                                                              1
                                                                        0.00002
                                                                               
                                                                        16.1328
                                                                              1
                                                                         0.0001
[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 Type-III Tests of Effect for the Full and Best-Fit Models  -  1,3-Butadiene (Bag 1).
Effect
                                       
                                  Full Model

                             Best-Fit Model (FM3)

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

Estimate
Std.Err.
d.f.
t-value
Pr>t
Intercept
                                                                               
                                                                        -5.9175
                                                                         0.1131
                                                                           5.02
                                                                         -50.97
                                                                     0.00000005

                                                                        -5.9175
                                                                         0.1159
                                                                           5.02
                                                                         -51.04
                                                                      0.0000005
Ze
                                                                               
                                                                        -0.1210
                                                                        0.03986
                                                                          57.04
                                                                          -3.04
                                                                         0.0036

                                                                        -0.1273
                                                                        0.03851
                                                                          57.05
                                                                          -3.30
                                                                         0.0017
Za
                                                                               
                                                                       -0.02730
                                                                        0.03496
                                                                          57.06
                                                                          -0.78
                                                                           0.44

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
Z5
                                                                               
                                                                         0.0441
                                                                        0.03887
                                                                          57.04
                                                                           1.14
                                                                           0.26

                                                                         003968
                                                                        0.03851
                                                                          57.04
                                                                           1.03
                                                                           0.31
Z9
                                                                               
                                                                       -0.01715
                                                                        0.03389
                                                                          57.10
                                                                          -0.51
                                                                           0.61

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                        0.06188
                                                                               
                                                                               
                                                                               
                                                                               

                                                                        0.06161
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                        0.06801
                                                                               
                                                                               
                                                                               
                                                                               

                                                                        0.06898