Document ID: EPA-HQ-OAR-2011-0135-0659
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 J.6
                              Final Model Fitting
                        Particulate Matter (PM) (Bag 3)

No. Observations:			   871
No. Vehicles:		  		     15   
No. censored measurements:		     82
No. missing measurements:		       2
No. measurements removed:		       1
Model Type:				Tobit regression

J.6.1  Model Fitting based on the 11-term design model.

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

                                       
                                     Full
                                    FM1[1]
                                      FM2
                                      FM3
                                      FM4
                                      FM5
                                     etOH
Ze
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                     Arom
Za
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      RVP
Zr
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      T50
Z5
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      T90
Z9
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
                                 etOH x etOH
ZZee
                                      ●
                                      ●
                                      x
                                       
                                       
                                       
                                  T50 x T50
ZZ55
                                      ●
                                      ●
                                      ●
                                      x
                                       
                                       
                                 etOH x Arom
ZZea
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                  etOH x RVP
ZZer
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
                                       
                                  etOH x T50
ZZe5
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                  etOH x T90
ZZe9
                                      ●
                                      x
                                       
                                       
                                       
                                       

1 Indicates "Full minus 1," etc.

  PM (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
                                   3224.082

                                                                               
                                                                               
                                                                               
FM1
                                                                             10
                                   3224.175

                                     0.093
                                       1
                                     0.760
FM2
                                                                              9
                                   3224.623

                                     0.448
                                       1
                                     0.503
FM3
                                                                              8
                                    3224.86

                                     0.237
                                       1
                                     0.626
FM4
                                                                              7
                                   3225.436

                                     0.576
                                       1
                                     0.448
FM5
                                                                              6
                                   3226.131

                                     0.695
                                       1
                                     0.404

                                                                               

                                                                               
                                                                               
                                                                               
[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.

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

J.6.2 Model Fitting based on the 17-term extended model.

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

                                       
                                     Full
                                    FM4[1]
                                      FM5
                                      FM6
                                      FM7
                                      FM8
                                      FM9
                                     FM10
                                     etOH
Ze
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                     Arom
Za
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      RVP
Zr
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      T50
Z5
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      T90
Z9
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
                                 etOH x etOH
ZZee
                                      ●
                                      ●
                                      x
                                       
                                       
                                       
                                       
                                       
                                  T50 x T50
ZZ55
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
                                       
                                       
                                       
                                 etOH x Arom
ZZea
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                  etOH x RVP
ZZer
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
                                       
                                       
                                  etOH x T50
ZZe5
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                  etOH x T90
ZZe9
                                      ●
                                      ●
                                      ●
                                      x
                                       
                                       
                                       
                                       
                                       

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

1 Indicates "Full minus 4," etc.

 PM (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
                                                                             17
                                   3215.611

                                                                               
                                                                               
                                                                               
FM4
                                                                             13
                                   3215.883

                                     0.272
                                       4
0.992
FM5
                                                                             12
                                   3216.627

                                     0.744
                                       1
0.388
FM6
                                                                             11
                                   3217.959

                                     1.332
                                       1
0.248
FM7
                                                                             10
                                   3219.173

                                     1.214
                                       1
0.271
FM8
                                                                              9
                                   3220.762

                                     1.589
                                       1
0.207
FM9
                                                                              8
                                   3222.431

                                     1.669
                                       1
0.196
FM10
                                                                              7
                                   3222.609

                                     0.178
                                       1
0.673

                                                                               

                                                                               
                                                                               
                                                                               
[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.

PM (Bag 3): Coefficients and Tests of Effect for the Full and Reduced Models, with respect to the 17-term extended model.