Document ID: EPA-HQ-OAR-2011-0135-0591
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  Q.3
                                       
                                       
                         Model Fitting Information for
                                Ethane (Bag 1)

This appendix suFMarizes model fitting for Bag-1 Ethane.  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 Bag-1 Ethane
Model Term
                                   Notation
                                     Model

                                       
                             Linear Effects (Full)
FM1
FM2
                                     etOH
Ze
                                      ●
                                      ●
                                      x
                                     Arom
Za
                                      ●
                                      ●
                                      ●
                                      T50
Z5
                                      ●
                                      ●
                                      ●
                                      T90
Z9
                                      ●
                                      x
                                       

 Fitting history for Bag-1 Ethane  -  with "FM1" 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]
Linear Effects
5
                                                                         -19.51
                                                                          -8.24

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
FM1
4
                                                                         -19.13
                                                                          -9.48

                                                                         0.3730
                                                                              1
                                                                           0.54
                                                                               
                                                                               
                                                                               
                                                                               
FM2
3
                                                                         -15.29
                                                                          -7.25

                                                                         4.2128
                                                                              2
                                                                           0.12
                                                                               
3.84
                                                                              1
                                                                          0.050
[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  -  Ethane (Bag 1).
Effect
                                       
                                  Full Model

                             Best-Fit Model (FM1)

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

Estimate
Std.Err.
d.f.
t-value
Pr>t
Intercept
                                                                               
                                                                        -4.3412
                                                                         0.2224
                                                                           5.00
                                                                         -19.52
                                                                    <0.00001

                                                                        -4.3412
                                                                         0.2226
                                                                           5.01
                                                                         -19.50
                                                                    <0.00001
Ze
                                                                               
                                                                        0.05357
                                                                        0.02621
                                                                          57.00
                                                                           2.04
                                                                          0.046

                                                                        0.05222
                                                                        0.02620
                                                                          57.00
                                                                           1.99
                                                                          0.051
Za
                                                                               
                                                                        -0.1912
                                                                        0.02298
                                                                          57.01
                                                                          -8.32
                                                                    <0.00001

                                                                        -0.1925
                                                                        0.02296
                                                                          57.01
                                                                          -8.39
                                                                    <0.00001
Z5
                                                                               
                                                                         0.1833
                                                                        0.02555
                                                                          57.00
                                                                           7.17
                                                                    <0.00001

                                                                         0.1830
                                                                        0.02563
                                                                          57.00
                                                                           7.14
                                                                    <0.00001
Z9
                                                                               
                                                                        0.01363
                                                                        0.02228
                                                                          57.01
                                                                           0.61
                                                                           0.54

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                         0.2448
                                                                               
                                                                               
                                                                               
                                                                               

                                                                         0.2454
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                        0.02939
                                                                               
                                                                               
                                                                               
                                                                               

                                                                        0.02958