Document ID: EPA-HQ-OAR-2011-0135-0618
Agency: epa
Document Type: Supporting & Related Material
Title: 
Posted Date: 2013-04-17T04:00Z

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 G.5
                              Final Model Fitting
                       Oxides of Nitrogen (NOx) (Bag 3)

No. Observations:			   931
No. Vehicles:		  		     15   
No. censored measurements:		     25
No. missing measurements:		       2
No. measurements removed:		       1
Model Type:				Tobit regression

G.5.1  Model Fitting based on the 11-term design model.

    Models fit for NOx (Bag 3): (Grand Intercept not fit by Tobit models).
Model Term
                                   Notation
                                     Model

                                       
                                     Full
                                    FM2[1]
                                      FM3
                                      FM4
                                      FM5
                                      FM6
                                      FM7
                                     etOH
Ze
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                     Arom
Za
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      RVP
Zr
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      T50
Z5
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
                                      T90
Z9
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                 etOH x etOH
ZZee
                                      ●
                                      x
                                       
                                       
                                       
                                       
                                       
                                  T50 x T50
ZZ55
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
                                       
                                       
                                 etOH x Arom
ZZea
                                      ●
                                      ●
                                      ●
                                      x
                                       
                                       
                                       
                                  etOH x RVP
ZZer
                                      ●
                                      x
                                       
                                       
                                       
                                       
                                       
                                  etOH x T50
ZZe5
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
                                       
                                  etOH x T90
ZZe9
                                      ●
                                      ●
                                      x
                                       
                                       
                                       
                                       

1 Indicates "Full minus 2," etc.

  NOx (Bag 3): Model fitting history, starting with the 11-term design model.
                                Fit Parameters

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

                                                                           Dev.
                                                                              d
                                                                    Pr>χ[2]
Full Model
                                                                             11
                                   2809.349

                                                                               
                                                                               
                                                                               
FM2
                                                                              9
                                   2809.676

                                     0.327
                                       2
                                     0.849
FM3
                                                                              8
                                   2810.499

                                     0.823
                                       1
                                     0.364
FM4
                                                                              7
                                   2811.808

                                     1.309
                                       1
                                     0.253
FM5
                                                                              6
                                   2813.571

                                     1.763
                                       1
                                     0.184
FM6
                                                                              5
                                   2815.925

                                     2.354
                                       1
                                     0.125
FM7
                                                                              4
                                   2817.195

                                     1.270
                                       1
                                     0.260

                                                                               

                                                                               
                                                                               
                                                                               
[1] Total number of terms excludes the intercept, as the Tobit
models do not fit intercepts.
[2] Best fit with respect to the 16-term extended model.

NOx (Bag 3): Coefficients and Tests of Effect for the Full and Reduced Models, with respect to the 11-term design model.

G.5.2 Model Fitting based on the 16-term extended model.

    Models fit for NOx (Bag 3): (Grand Intercept not fit by Tobit models).
Model Term
                                   Notation
                                     Model

                                       
                                     Full
                                    FM4[1]
                                      FM5
                                      FM6
                                      FM7
                                      FM8
                                      FM9
                                     etOH
Ze
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                     Arom
Za
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      RVP
Zr
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      T50
Z5
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      T90
Z9
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                 etOH x etOH
ZZee
                                      ●
                                      x
                                       
                                       
                                       
                                       
                                       
                                  T50 x T50
ZZ55
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
                                 etOH x Arom
ZZea
                                      ●
                                      ●
                                      x
                                       
                                       
                                       
                                       
                                  etOH x RVP
ZZer
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
                                       
                                       
                                  etOH x T50
ZZe5
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                  etOH x T90
ZZe9
                                      ●
                                      ●
                                      ●
                                      x
                                       
                                       
                                       
                                       

                                       
                                       
                                       
                                       
                                       
                                       
                                       
                                  T90 x T90
ZZ99
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                  Arom x RVP
ZZar
                                      ●
                                      x
                                       
                                       
                                       
                                       
                                       
                                  Arom x T50
ZZa5
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                  Arom x T90
ZZa9
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
                                       
                                  T50 x T90
ZZ59
                                      ●
                                      x
                                       
                                       
                                       
                                       
                                       
                                  RVP x T90
ZZr9
                                      ●
                                      x
                                       
                                       
                                       
                                       
                                       

 NOx (Bag 3): Model fitting history, starting with the 17-term extended model.
                                Fit Parameters

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

                                                                           Dev.
                                                                              d
                                                                    Pr>χ[2]
Full Model
                                                                             16
                                                                       2801.073

                                                                               
                                                                               
                                                                               
FM4
                                                                             12
                                                                       2801.869

                                     0.796
                                       4
                                     0.939
FM5
                                                                             11
                                                                       2802.472

                                     0.603
                                       1
                                     0.437
FM6
                                                                             10
                                                                       2803.337

                                     0.865
                                       1
                                     0.352
FM7
                                                                              9
                                                                       2804.295

                                     0.958
                                       1
                                     0.328
FM8
                                                                              8
                                                                       2806.313

                                     2.018
                                       1
                                     0.155
FM9
                                                                              7
                                                                       2808.530

                                     2.217
                                       1
                                     0.136

                                                                               

                                                                               
                                                                               
                                                                               
[1] Total number of terms excludes the intercept, as the Tobit
Models do not fit intercepts.
[2] Best fit with respect to the 17-term extended model.

NOx (Bag 3): Coefficients and Tests of Effect for the Full and Reduced Models, with respect to the 16-term extended model.