Document ID: EPA-HQ-OAR-2011-0135-0655
Agency: epa
Document Type: Supporting & Related Material
Title: 
Posted Date: 2013-04-18T04:00Z

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 I.2e
                              Final Model Fitting
                   Non-Methane Organic Gases (NMOG) (Bag 2)

No. Observations:			832
No. Vehicles:		  		  13   (exclude Odyssey and Sienna)
No. censored measurements:		    0
No. missing measurements:		    0
No. measurements removed:		    0
Model Type:				Mixed model

I.2e.1   Model fitting with respect to the 11-term design model.
Design Model (11-terms):  Bayesian Information Criterion (BIC) vs. number of terms in model (p) for all possible models respecting hierarchy. 

Design Model (11-terms):  Bayesian Information Criterion (BIC) vs. number of terms in model (p) for all possible models respecting hierarchy (CLOSEUP of previous figure). 

Design Model (11-terms):  Bayesian Information Criterion (BIC) vs. number of terms in model (p) for all possible models respecting hierarchy (CLOSEUP of previous figure). 

NMOG (Bag 2):  Number of terms (p), Goodness-of-fit (BIC) and terms included in the 35 best-fitting candidate models (out of a total of 294 possible models with hierarchy).  (Terms included in models ranked 1-8 comprise the "superset" for final model-fitting).

     Models fit for NMOG (Bag 2): (all models include an intercept term).
Model Term
                                   Notation
                                     Model

                                       
                                   Superset
                                    SM2[1]
                                      SM5
                                       
                                    SM4[2]
                                       
                                    SM3a[3]
                                       
                                    SM3b[4]
                                     etOH
Ze
                                      ●
                                      ●
                                      x
                                       
                                      ●
                                       
                                      ●
                                       
                                      ●
                                     Arom
Za
                                      ●
                                      ●
                                      ●
                                       
                                      ●
                                       
                                      ●
                                       
                                      ●
                                      RVP
Zr
                                      ●
                                      ●
                                      ●
                                       
                                      ●
                                       
                                      ●
                                       
                                      ●
                                      T50
Z5
                                      ●
                                      ●
                                      ●
                                       
                                      ●
                                       
                                      ●
                                       
                                      ●
                                      T90
Z9
                                      ●
                                      ●
                                      ●
                                       
                                      ●
                                       
                                      ●
                                       
                                      ●
                                 etOH x etOH
ZZee
                                      ---
                                      ---
                                      ---
                                       
                                      ---
                                       
                                      ---
                                       
                                      ---
                                  T50 x T50
ZZ55
                                      ●
                                      ●
                                      ●
                                       
                                      ●
                                       
                                      ●
                                       
                                      ●
                                 etOH x Arom
ZZea
                                      ●
                                      ●
                                      x
                                       
                                      x
                                       
                                      x
                                       
                                      ●
                                  etOH x RVP
ZZer
                                      ●
                                      x
                                       
                                       
                                       
                                       
                                       
                                       
                                       
                                  etOH x T50
ZZe5
                                      ●
                                      ●
                                      x
                                       
                                      x
                                       
                                      ●
                                       
                                      x
                                  etOH x T90
ZZe9
                                      ●
                                      x
                                       
                                       
                                       
                                       
                                       
                                       
                                       
                                       

                                       
                                       
                                       
                                       
                                       
                                       
                                       
                                       
                                       
[1] Represents "Superset minus 2," etc.
[2] Not nested within SM5; formed by dropping etOHxArom and etOHxT50 from SM2.
3 Not nested within SM5 or SM4; formed by dropping etOHxArom from SM2.
[4]Not nested within SM5, SM4 or SM3a; formed by dropping etOHxT50 from SM2.

NMOG (Bag 2): Model fitting history, starting with the 10-term superset model.
                                Fit Parameters

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

                                                                           Dev.
                                                                              d
                                                                    Pr>χ[2]
Superset
                                                                             11
745.891
779.235

                                                                               
                                                                               
                                                                               
SM2[2]
                                                                              9
748.716
776.930

                                                                          2.825
                                                                              2
                                                                          0.244
SM5
                                                                              6
757.086
777.605

                                                                          8.370
                                                                              3
                                                                         0.0390

                                                                               

                                                                               
                                                                               
                                                                               
SM4[3]
                                                                              7
754.855
777.940

                                                                          6.140
                                                                              2
                                                                         0.0464

                                                                               

                                                                               
                                                                               
                                                                               
SM3a[3]
                                                                              8
751.636
777.286

                                                                          2.920
                                                                              1
                                                                         0.0875

                                                                               

                                                                               
                                                                               
                                                                               
SM3b[3]
                                                                              8
751.934
777.584

                                                                          3.219
                                                                              1
                                                                         0.0728

                                                                               

                                                                               
                                                                               
                                                                               
[1] A lower value indicates a better fit.
[2] Best fit with respect to the 11-term design model.
[3] Not nested within previous model; test with respect to SM2.

NMOG (Bag 2): Coefficients  and Tests of Effect for the Superset and Reduced Models, with respect to the 11-term design model. 

I.2e.2	Model Fitting with respect to the 16-term extended Model.
Extended Model (16-terms):  Bayesian Information Criterion (BIC) vs. number of terms in model (p) for all possible models respecting hierarchy. 

Extended Model (16-terms):  Bayesian Information Criterion (BIC) vs. number of terms in model (p) for subset of models respecting hierarchy (CLOSEUP of previous figure).

Extended Model (16-terms):  Bayesian Information Criterion (BIC) vs. number of terms in model (p) for subset of models respecting hierarchy (CLOSEUP of previous figure).

NMOG (Bag 2):  Number of terms (p), Goodness-of-fit (BIC) and terms included in the 35 best-fitting candidate models (out of a total of 2,964 possible models with hierarchy).  (Terms included in models ranked 1-5 comprise the "superset" for final model-fitting).
 

     Models fit for NMOG (Bag 2): (all models include an intercept term).
Model Term
                                   Notation
                                     Model

                                       
                                   Superset
                                    SM1[1]
                                     etOH
Ze
                                      ●
                                      ●
                                     Arom
Za
                                      ●
                                      ●
                                      RVP
Zr
                                      ●
                                      ●
                                      T50
Z5
                                      ●
                                      ●
                                      T90
Z9
                                      ●
                                      ●
                                 etOH x etOH
ZZee
                                      ---
                                      ---
                                  T50 x T50
ZZ55
                                      ●
                                      ●
                                 etOH x Arom
ZZea
                                      ●
                                      ●
                                  etOH x RVP
ZZer
                                      ●
                                      ●
                                  etOH x T50
ZZe5
                                      ●
                                      ●
                                  etOH x T90
ZZe9
                                      ---
                                      ---
                                       

                                       
                                       
                                  Arom x RVP
ZZar
                                      ---
                                      ---
                                  Arom x T50
ZZa5
                                      ●
                                      ●
                                  Arom x T90
ZZa9
                                      ●
                                      x
                                  T50 x T90
ZZ59
                                      ---
                                      ---
                                  RVP x T90
ZZr9
                                      ---
                                      ---

[1] denotes "Superset minus 1, etc."

NMOG (Bag 2): Model fitting history, starting with the 9-term superset model.
                                Fit Parameters

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

                                                                           Dev.
                                                                              d
                                                                    Pr>χ[2]
Superset
                                                                             12
740.652
776.561

                                                                               
                                                                               
                                                                               
SM1
                                                                             11
742.372
775.716

                                                                          1.720
                                                                              1
                                                                          0.190

                                                                               

                                                                               
                                                                               
                                                                               
[1] A lower value indicates a better fit.
[2] Best fit with respect to the 16-term extended model.

NMOG (Bag 2): NMOGefficients  and Tests of Effect for the Superset and Reduced Models, with respect to the 16-term extended model.