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.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
2

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 FM11FM2 FM3 FM4 FM5

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 ● ×

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.
3

PM (Bag 3): Coefficients and Tests of Effect for the Full and Reduced Models, with respect to the 

11-term design model.

Effect Full Model Reduced Model (FM5)

Estimate Std. Err. d.f. χ

2

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

2

- value Pr>χ2

Intercept1-0.3539

Ze-0.0003 0.0656 1 0.000000 1.00 0.0173 0.0579 1 0.090 0.77

Za 0.0170 0.0457 1 0.140 0.71 0.0216 0.0455 1 0.220 0.64

Zr-0.1082 0.0522 1 4.30 0.038 -0.1098 0.0499 1 4.840 0.03

Z5 0.0079 0.0658 1 0.010 0.90 0.0167 0.0616 1 0.070 0.79

Z9-0.0337 0.0457 1 0.54 0.46

ZZee -0.0593 0.0879 1 0.46 0.50

ZZ55 -0.0527 0.0658 1 0.64 0.42

ZZea 0.0975 0.0447 1 4.76 0.029 0.1023 0.0441 1 5.390 0.02

ZZer -0.0402 0.0456 1 0.78 0.38

ZZe5 -0.1885 0.0943 1 4.00 0.046 -0.1218 0.0455 1 7.170 0.01

ZZe9 0.0136 0.0448 1 0.090 0.76

0.1178

1.3431

1

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

1 2

veh

2


4

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 FM41FM5 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 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.
5

PM (Bag 3): 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-0.0434 0.0810 1 0.29 0.59 -0.0212 0.0613 1 0.12 0.73

Za-0.0024 0.0552 1 0.0000 0.97 0.0186 0.0455 1 0.17 0.68

Zr-0.1395 0.0754 1 3.42 0.06 -0.1275 0.0507 1 6.33 0.012

Z5-0.0311 0.1081 1 0.080 0.77 -0.0411 0.0687 1 0.36 0.55

Z9 0.0031 0.0593 1 0.000000 0.96

ZZee -0.0751 0.0919 1 0.67 0.41

ZZ55 -0.1023 0.0750 1 1.86 0.17

ZZea 0.0544 0.0748 1 0.53 0.47 0.0849 0.0450 1 3.57 0.059

ZZer -0.0742 0.0506 1 2.15 0.14

ZZe5 -0.1512 0.0970 1 2.43 0.12 -0.0824 0.0500 1 2.71 0.10

ZZe9 0.0399 0.0617 1 0.42 0.52

ZZar -0.1631 0.0944 1 2.99 0.08 -0.1062 0.0566 1 3.53 0.060

ZZa5 -0.0107 0.1016 1 0.010 0.92

ZZa9 0.0892 0.0515 1 3.01 0.08

ZZ59 -0.0241 0.0670 1 0.13 0.72

ZZr9 0.00020 0.0582 1 0.000000 1.00

1.3351 1.3405

1

 Not fit by Tobit model.

1 2

veh

2

