Document ID: EPA-HQ-OAR-2011-0135-0596
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  N.4
                                       
                                       
                         Model Fitting Information for
                                Ethanol (Bag 2)

This appendix summarizes model fitting for Bag-2 Ethanol.  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:	63
No. censored values:	24
Modeling approach:	TOBIT REGRESSION
Estimated Dependent Variable model:	YES

Models fit for Ethanol, Bag 2 (all models include an intercept term) 
Model term
                                   Notation
                                     Model

                                       
                              Full (Main Effects)
MM1
MM3
Null model
                                     etOH
Ze
                                      ●
                                      ●
                                      ●
                                       
                                     Arom
Za
                                      ●
                                      ●
                                      x
                                       
                                      RVP
Zr
                                       
                                       
                                       
                                       
                                      T50
Z5
                                      ●
                                      x
                                       
                                       
                                      T90
Z9
                                      ●
                                      ●
                                      x
                                       

 Model Fitting History for Ethanol, Bag 2 (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]
Full
                                                                              4
79.744

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
MM1
                                                                              3
79.749

                                                                        0.00610
                                                                              1
                                                                           0.94
                                                                               
                                                                               
                                                                               
                                                                               
MM3
                                                                              1
83.475

                                                                          3.731
                                                                              3
                                                                           0.29
                                                                               
                                                                          3.725
                                                                              2
                                                                           0.16
Null model
                                                                              0
92.339

                                                                         12.595
                                                                              4
                                                                           0.01
                                                                               
                                                                          8.864
                                                                              1
                                                                         0.0029
[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  Tests of Effect for the Full and Best-Fit Models  -  Ethanol (Bag 2).
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[1]
                                                                               
                                    -9.3072
                                                                         0.6333
                                                                              5
                                                                         -15.45
                                                                       0.000021

                                                                        -9.5634
                                                                         0.6703
                                                                              5
                                                                         -14.64
                                                                        0.00002
Ze
                                                                               
                                                                         0.9233
                                                                         0.2824
                                                                              5
                                                                           3.27
                                                                          0.022

                                                                         0.8163
                                                                         0.2805
                                                                              5
                                                                           2.91
                                                                          0.033
Za
                                                                               
                                                                        -0.3772
                                                                        0.28499
                                                                              5
                                                                          -1.32
                                                                           0.24

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
Z5
                                                                               
                                                                        -.01910
                                                                         0.2091
                                                                              5
                                                                         -0.091
                                                                           0.93

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
Z9
                                                                               
                                                                        -0.3017
                                                                         0.2416
                                                                              5
                                                                          -1.25
                                                                           0.27

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
[1]
                                                                               
                                                                         0.3707
                                                                               
                                                                               
                                                                               
                                                                               

                                                                         0.4634
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                         1.0889
                                                                               
                                                                               
                                                                               
                                                                               

                                                                         1.1682
                                                                               
                                                                               
                                                                               
                                                                               
[1] Not fit by the model, but manually recalculated from intercepts for individual vehicles.