Document ID: EPA-HQ-OAR-2011-0135-0601
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.4
                                       
                                       
                         Model Fitting Information for
                                Ethane (Bag 2)

This appendix summarizes model fitting for Bag-2 Ethane.  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:	62
No. censored values:	1
Modeling approach:	MIXED MODEL
Estimated Dependent Variable model:	NO

                          Models fit for Bag-2 Ethane
Model term
                                   Notation
                                     Model

                                       
                                     Full
                                      FM1
                                     etOH
Ze
                                      ●
                                      x
                                     Arom
Za
                                      ●
                                      ●
                                      T50
Z5
                                      ●
                                      ●
                                      T90
Z9
                                      ●
                                      ●
                                       

                                       
                                       
[1] Indicates "Full minus 1," etc.

Fitting history for Bag-2 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]
Full
5
84.42
95.68

                                                                         0.6829
                                                                              1
                                                                           0.41
                                                                               
                                                                               
                                                                               
                                                                               
FM1
4
85.96
95.62

                                                                         2.2256
                                                                              2
                                                                           0.33
                                                                               
                                                                           1.54
                                                                              1
                                                                           0.21
[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 2).
Effect
                                       
                                  Full Model

                             Best-Fit Model (MM1)

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

Estimate
Std.Err.
d.f.
t-value
Pr>t
Intercept
                                                                               
                                                                        -7.7241
                                                                         0.7325
                                                                           5.00
                                                                          -10.5
                                                                        0.00013

                                                                        -7.7241
                                                                         0.7320
                                                                           5.00
                                                                         -10.55
                                                                        0.00013
Ze
                                                                               
                                                                        0.07345
                                                                        0.05873
                                                                          57.00
                                                                           1.25
                                                                           0.22

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
Za
                                                                               
                                                                        -0.1260
                                                                        0.05151
                                                                          57.00
                                                                          -2.45
                                                                          0.018

                                                                        -0.1092
                                                                        0.05041
                                                                          57.00
                                                                          -2.17
                                                                          0.034
Z5
                                                                               
                                                                         0.1815
                                                                        0.05727
                                                                          57.00
                                                                           3.17
                                                                         0.0025

                                                                         0.1452
                                                                        0.05006
                                                                          57.00
                                                                           2.90
                                                                         0.0053
Z9
                                                                               
                                                                         0.1322
                                                                        0.04994
                                                                          57.00
                                                                           2.65
                                                                          0.010

                                                                         0.1270
                                                                        0.05044
                                                                          57.00
                                                                           2.52
                                                                          0.015

                                                                               
                                                                         2.6785
                                                                               
                                                                               
                                                                               
                                                                               

                                                                         2.6669
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                         0.1458
                                                                               
                                                                               
                                                                               
                                                                               

                                                                         0.1517