Document ID: EPA-HQ-OAR-2011-0135-0658
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.5
                              Final Model Fitting
                        Particulate Matter (PM) (Bag 2)

No. Observations:			   906
No. Vehicles:		  		     15   
No. censored measurements:		     47
No. missing measurements:		       2
No. measurements removed:		       1
Model Type:				Tobit regression

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

     Models fit for PM (Bag 2): (Grand Intercept not fit by Tobit models).
Model Term
                                   Notation
                                     Model

                                       
                                     Full
                                    FM3[1]
                                      FM4
                                      FM5
                                      FM6
                                      FM7
                                      FM8
                                     etOH
Ze
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                     Arom
Za
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      RVP
Zr
                                      ●
                                      ●
                                      ●
                                      x
                                       
                                       
                                       
                                      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
                                      ●
                                      ●
                                      ●
                                      ●
                                       
                                       
                                       
                                  etOH x T90
ZZe9
                                      ●
                                      x
                                       
                                       
                                       
                                       
                                       

  PM (Bag 2): 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
                                                                       2954.321

                                                                               
                                                                               
                                                                               
FM3
                                                                              8
                                                                       2954.834

0.513
                                                                              3
0.916
FM4
                                                                              7
                                                                       2955.471

0.637
                                                                              1
0.425
FM5
                                                                              6
                                                                       2957.466

1.995
                                                                              1
0.158
FM6
                                                                              5
                                                                       2959.590

2.124
                                                                              1
0.145
FM7
                                                                              4
                                                                       2959.643

0.053
                                                                              1
0.818
FM8
                                                                              3
                                                                       2961.414

1.771
                                                                              1
0.183

                                                                               

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

J.5.2 Model Fitting based on the 17-term extended model.

     Models fit for PM (Bag 2): (Grand Intercept not fit by Tobit models).
Model Term
                                   Notation
                                     Model

                                       
                                     Full
                                    FM4[1]
                                      FM5
                                      FM6
                                      FM7
                                      FM8
                                      FM9
                                     FM10
                                     FM11
                                     FM12
                                     etOH
Ze
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                     Arom
Za
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      RVP
Zr
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
                                       
                                       
                                      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
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
                                       
                                  etOH x T90
ZZe9
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
                                       
                                       
                                       
                                       

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

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

 PM (Bag 2): 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
                                   2937.842

                                                                               
                                                                               
                                                                               
FM4
                                                                             13
                                   2938.618

0.776
4
0.9416
FM5
                                                                             12
                                   2939.112

0.494
1
0.4821
FM6
                                                                             11
                                   2941.062

1.950
1
0.1626
FM7
                                                                             10
                                   2943.444

2.382
1
0.1227
FM8
                                                                              9
                                   2945.255

1.811
1
0.1784
FM9
                                                                              8
                                   2947.232

1.977
1
0.1597
FM10
                                                                              7
                                   2949.896

2.664
1
0.1026
FM11
                                                                              6
                                   2952.334

2.438
1
0.1184
FM12[2]
                                                                              5
                                   2954.483

2.149
1
0.1427

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