Document ID: EPA-HQ-OAR-2011-0135-0599
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  O.3
                                       
                                       
                         Model Fitting Information for
                                Benzene (Bag 1)

This appendix summarizes model fitting for Bag-1 Benzene.  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:	REDUCED
Media contamination:	NO
No. measurements:	176
No. censored values:	0
Modeling approach:	MIXED MODEL
Estimated Dependent Variable model:	NO

Models fit for Bag-1 Benzene
Model Term
                                   Notation
                                     Model

                                       
                              Main Effects (Full)
MM2
MM3
                                     etOH
Ze
                                      ●
                                      x
                                       
                                     Arom
Za
                                      ●
                                      ●
                                      ●
                                      RVP
Zr
                                       
                                       
                                       
                                      T50
Z5
                                      ●
                                      ●
                                      x
                                      T90
Z9
                                      ●
                                      x
                                       

 Fitting history for Bag-1 Benzene  -  with "MM3" 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]
Main Effects
5
                                                                         248.12
                                                                         267.08

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
MM2
3
                                                                         248.27
                                                                         261.81

                                                                          0.144
                                                                              2
                                                                           0.93
                                                                               
                                                                               
                                                                               
                                                                               
MM3
2
                                                                         250.02
                                                                         260.85

                                                                           1.89
                                                                              3
                                                                           0.59
                                                                               
                                                                           1.75
                                                                              1
                                                                           0.19
[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  -  Benzene (Bag 1).
Effect
                                       
                                  Full Model

                             Best-Fit Model (MM3)

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

Estimate
Std.Err.
d.f.
t-value
Pr>t
Intercept
                                                                               
                                                                        -4.1019
                                                                         0.1392
                                                                          15.07
                                                                         -29.48
                                                                     <0.0001

                                                                        -4.1074
                                                                         0.1391
                                                                          15.05
                                                                         -29.52
                                                                     <0.0001
Ze
                                                                               
                                                                      -0.004685
                                                                        0.03704
                                                                         161.12
                                                                         -0.126
                                                                           0.90

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
Za
                                                                               
                                                                         0.4056
                                                                        0.03389
                                                                         161.17
                                                                          11.97
                                                                     <0.0001

                                                                         0.4032
                                                                        0.03284
                                                                         161.20
                                                                          12.28
                                                                     <0.0001
Z5
                                                                               
                                                                        0.04142
                                                                        0.03789
                                                                         161.15
                                                                           1.09
                                                                           0.28

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
Z9
                                                                               
                                                                        0.01133
                                                                        0.03255
                                                                         161.20
                                                                           0.35
                                                                           0.73

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                         0.2741
                                                                               
                                                                               
                                                                               
                                                                               

                                                                         0.2739
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                         0.1873
                                                                               
                                                                               
                                                                               
                                                                               

                                                                         0.1896