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	G.5

Final	Model	Fitting

Oxides	of	Nitrogen (NOx)	(Bag	3)

No. Observations: 931

No. Vehicles: 15 

No. censored measurements: 25

No. missing measurements: 2

No. measurements removed: 1

Model Type: Tobit regression
2

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

Models fit for NOx (Bag 3): (Grand Intercept not fit by Tobit models).

Model Term Notation Model

Full FM21FM3 FM4 FM5 FM6 FM7

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 2,” etc.

NOx (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 2809.349

FM2 9 2809.676 0.327 2 0.849

FM3 8 2810.499 0.823 1 0.364

FM4 7 2811.808 1.309 1 0.253

FM5 6 2813.571 1.763 1 0.184

FM6 5 2815.925 2.354 1 0.125

FM7 4 2817.195 1.270 1 0.260

1 Total number of terms excludes the intercept, as the Tobit

models do not fit intercepts.

2 Best fit with respect to the 16-term extended model.
3

NOx (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 (FM7)

Estimate Std. Err. d.f. χ

2

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

2

- value Pr>χ2

Intercept1-5.2561

Ze

0.06820 0.05120 1 1.77 0.18 0.1078 0.0348 1 9.59 0.0020

Za

0.06770 0.03570 1 3.59 0.058 0.0816 0.0350 1 5.42 0.020

Zr

0.11760 0.04080 1 8.30 0.0040 0.1477 0.0356 1 17.2 <0.0001

Z5

-0.05780 0.05140 1 1.26 0.26

Z9

0.06850 0.03570 1 3.68 0.055 0.0601 0.0353 1 2.90 0.089

ZZee -0.01240 0.06870 1 0.03 0.86

ZZ55 0.05010 0.05150 1 0.95 0.33

ZZea -0.04210 0.03490 1 1.45 0.23

ZZer -0.02020 0.03570 1 0.32 0.57

ZZe5 0.06420 0.07380 1 0.76 0.38

ZZe9 0.03450 0.03510 1 0.97 0.33

1.7619

1.05310 1.05750

1

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

1 2

veh

2


4

G.5.2	Model	Fitting	based	on	the	16-term	extended	model.

Models fit for NOx (Bag 3): (Grand Intercept not fit by Tobit models).

Model Term Notation Model

Full FM41FM5 FM6 FM7 FM8 FM9

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 ● ×

NOx (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 16 2801.073

FM4 12 2801.869 0.796 4 0.939

FM5 11 2802.472 0.603 1 0.437

FM6 10 2803.337 0.865 1 0.352

FM7 9 2804.295 0.958 1 0.328

FM8 8 2806.313 2.018 1 0.155

FM9 7 2808.530 2.217 1 0.136

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

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

16-term extended model.

Effect Full Model Reduced Model (FM9)

Estimate Std. Err. d.f. χ

2

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

2

- value Pr>χ2

Intercept1-5.255

Ze 0.0693 0.0616 1.0000 1.26 0.261 0.0884 0.0453 1 3.82 0.051

Za 0.0661 0.0387 1.0000 2.92 0.088 0.0667 0.0356 1 3.52 0.061

Zr 0.1737 0.0520 1.0000 11.1 0.00080 0.1692 0.0420 1 16.2 <0.0001

Z5-0.0508 0.0686 1.0000 0.55 0.46 -0.0224 0.0488 1 0.21 0.65

Z9 0.1007 0.0398 1.0000 6.39 0.012 0.0850 0.0366 1 5.39 0.020

ZZee -0.0220 0.0718 1.0000 0.09 0.76

ZZ55 0.0553 0.0586 1.0000 0.89 0.34

ZZea 0.0477 0.0581 1.0000 0.67 0.41

ZZer -0.0516 0.0394 1.0000 1.72 0.19

ZZe5 0.0654 0.0758 1.0000 0.74 0.39 0.0637 0.0358 1 3.16 0.075

ZZe9 0.0464 0.0466 1.0000 0.99 0.32

ZZar 0.0254 0.0630 1.0000 0.16 0.69

ZZa5 0.1624 0.0701 1.0000 5.36 0.021 0.0894 0.0398 1 5.05 0.025

ZZa9 -0.0444 0.0394 1.0000 1.27 0.26

ZZ59 0.0226 0.0524 1.0000 0.19 0.67

ZZr9 0.0300 0.0446 1.0000 0.45 0.50

1.7509

1.0486 1.0527

1

 Not fit by Tobit model.

1 2

veh

2 