1

Assessing	the	Effect	of	Five	Gasoline	Properties	on	Exhaust	Emissions	from	LightDuty	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
2

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 FM21FM3 FM4 FM5 FM6

etOH Ze ● ● ● ● ● ●

Arom Za ● ● ● ● ● ●

RVP Zr ● ● ● ● ● ×

T50 Z5 ● ● ● ● ● ●

T90 Z9 ● ● ● ● ● ●

etOH × etOH ZZee ● ×

T50 × T50 ZZ55 ● ● ● ● ● ●

etOH × Arom ZZea ● ● ● ×

etOH × RVP ZZer ● ● ×

etOH × T50 ZZe5 ● ×

etOH × T90 ZZe9 ● ● ● ● ×

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

FM625 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.
3

PM (Bag 1): Coefficients and Tests of Effect for the Full and Reduced Models, with respect to the 

11-term design model.

Effect Full Model Reduced Model (FM6)

Estimate Std. Err. d.f. χ

2

- value Pr>χ2Estimate Std. Err. d.f. χ

2

- value Pr>χ2

Intercept10.6559

Ze 0.1365 0.05030 1 7.35 0.0067 0.1582 0.04130 1 14.7 0.00010

Za 0.3840 0.03510 1 119.96 <.0001 0.3833 0.03480 1 121 <.0001

Zr-0.0227 0.04000 1 0.32 0.57

Z5 0.0338 0.05050 1 0.45 0.50 0.0550 0.04310 1 1.63 0.20

Z9 0.2965 0.03510 1 71.48 <.0001 0.2923 0.03440 1 72.2 <.0001

ZZee -0.0401 0.06750 1 0.35 0.55

ZZ55 0.0700 0.05050 1 1.92 0.166 0.0935 0.03420 1 7.46 0.0063

ZZea 0.0508 0.03430 1 2.19 0.139

ZZer 0.0295 0.03500 1 0.71 0.40

ZZe5 -0.0482 0.07230 1 0.44 0.51

ZZe9 0.0503 0.03440 1 2.14 0.14

0.4251

1.0321 1.0359

1

Not fit by Tobit model; calculated manually from individual vehicle intercepts.

1 2

veh

2


4

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 FM31FM5 FM6 FM7 FM8 FM9 FM10

etOH Ze ● ● ● ● ● ● ● ●

Arom Za ● ● ● ● ● ● ● ●

RVP Zr ● ● ● ● ● ● ● ×

T50 Z5 ● ● ● ● ● ● ● ●

T90 Z9 ● ● ● ● ● ● ● ●

etOH × etOH ZZee ● ×

T50 × T50 ZZ55 ● ● ● ● ● ● ● ●

etOH × Arom ZZea ● ● ● ● ● ● ×

etOH × RVP ZZer ● ×

etOH × T50 ZZe5 ● ● ×

etOH × T90 ZZe9 ● ● ● ● ● ● ● ●

T90 × T90 ZZ99 ● ● ● ● ×

Arom × RVP ZZar ● ● ● × ● ● ● ●

Arom × T50 ZZa5 ● ×

Arom × T90 ZZa9 ● ● ● ● ● ● ● ●

T50 × T90 ZZ59 ● ● ×

RVP × T90 ZZr9 ● ● ● ● ● ×

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

FM1027 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.
5

PM (Bag 1): Coefficients and Tests of Effect for the Full and Reduced Models, with respect to the 

17-term extended model.

Effect Full Model Reduced Model (FM10)

Estimate Std. Err. d.f. χ

2

- value Pr>χ2Estimate Std. Err. d.f. χ

2

- value Pr>χ2

Intercept1

Ze 0.1512 0.0628 1 5.80 0.016 0.1807 0.0425 1 18.0 <.0001

Za 0.4355 0.0428 1 104 <.0001 0.3792 0.0351 1 116.6 <.0001

Zr-0.0619 0.0585 1 1.12 0.2897

Z5 0.0047 0.0837 1 0.00000 0.96 0.1004 0.0470 1 4.6 0.0326

Z9 0.3494 0.0459 1 58.0 <.0001 0.3034 0.0353 1 74.0 <.0001

ZZee -0.0213 0.0712 1 0.090 0.7653

ZZ55 0.0790 0.0582 1 1.84 0.17 0.0806 0.0346 1 5.4 0.0198

ZZea 0.0682 0.0579 1 1.39 0.24

ZZer 0.0119 0.0392 1 0.090 0.76

ZZe5 -0.0452 0.0752 1 0.36 0.55

ZZe9 0.1018 0.0478 1 4.53 0.033 0.0647 0.0349 1 3.4 0.0636

ZZar -0.0602 0.0731 1 0.68 0.41

ZZa5 -0.0340 0.0788 1 0.19 0.67

ZZa9 0.0551 0.0399 1 1.91 0.17 0.0665 0.0380 1 3.1 0.0804

ZZ59 0.0389 0.0520 1 0.560 0.45

ZZr9 -0.0558 0.0452 1 1.53 0.22

1.0443

1

 Not fit by Tobit model.

1 2

veh

2

