Document ID: EPA-HQ-OAR-2011-0135-0657
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.4
                              Final Model Fitting
                        Particulate Matter (PM) (Bag 1)

No. Observations:			   910
No. Vehicles:		  		     15   
No. censored measurements:		     45
No. missing measurements:		       0
No. measurements removed:		       1
Model Type:				Tobit regression

J.4.1  Model Fitting based on the 11-term design model.

     Models fit for PM (Bag 1): (Grand Intercept not fit by Tobit models).
Model Term
                                   Notation
                                     Model

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

  PM (Bag 1): 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
                                                                       2789.671

                                                                               
                                                                               
                                                                               
FM2
                                                                              9
                                                                       2790.118

0.447
                                                                              2
0.800
FM3
                                                                              8
                                                                       2791.074

0.956
                                                                              1
0.328
FM4
                                                                              7
                                                                       2793.414

2.34
                                                                              1
0.126
FM5
                                                                              6
                                                                       2796.069

2.655
                                                                              1
0.103
FM6[2]
                                                                              5
                                                                       2796.308

0.239
                                                                              1
0.625

                                                                               

                                                                               
                                                                               
                                                                               
[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 1): Coefficients and Tests of Effect for the Full and Reduced Models, with respect to the 11-term design model.

J.4.2 Model Fitting based on the 17-term extended model.

     Models fit for PM (Bag 1): (Grand Intercept not fit by Tobit models).
Model Term
                                   Notation
                                     Model

                                       
                                     Full
                                    FM3[1]
                                      FM5
                                      FM6
                                      FM7
                                      FM8
                                      FM9
                                     FM10
                                     etOH
Ze
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                     Arom
Za
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      RVP
Zr
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
                                      T50
Z5
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      T90
Z9
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                 etOH x etOH
ZZee
                                      ●
                                      x
                                       
                                       
                                       
                                       
                                       
                                       
                                  T50 x T50
ZZ55
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                 etOH x Arom
ZZea
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
                                       
                                  etOH x RVP
ZZer
                                      ●
                                      x
                                       
                                       
                                       
                                       
                                       
                                       
                                  etOH x T50
ZZe5
                                      ●
                                      ●
                                      x
                                       
                                       
                                       
                                       
                                       
                                  etOH x T90
ZZe9
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                       

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

[1] Indicates "Full minus 3," etc.

 PM (Bag 1): 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
                                                                       2804.455

                                                                               
                                                                               
                                                                               
FM3
                                                                             14
                                                                       2804.778

0.323
                                                                              3
0.956
FM5
                                                                             12
                                                                       2805.586

0.808
                                                                              2
0.668
FM6
                                                                             11
                                                                       2806.743

1.157
                                                                              1
0.282
FM7
                                                                             10
                                                                       2809.264

2.521
                                                                              1
0.112
FM8
                                                                              9
                                                                       2811.736

2.472
                                                                              1
0.116
FM9
                                                                              8
                                                                       2813.991

2.255
                                                                              1
0.133
FM10[2]
                                                                              7
                                                                       2814.388

0.397
                                                                              1
0.529

                                                                              7

                                                                               
                                                                               
                                                                               
[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 1): Coefficients and Tests of Effect for the Full and Reduced Models, with respect to the 17-term extended model.