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.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
2

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 FM31FM4 FM5 FM6 FM7 FM8

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 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.
3

PM (Bag 2): Coefficients and Tests of Effect for the Full and Reduced Models, with respect to the 

11-term design model.

Effect Full Model Reduced Model (FM8)

Estimate Std. Err. d.f. χ

2

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

2

- value Pr>χ2

Intercept1-1.3107

Ze 0.0390 0.0552 1 0.500 0.48 0.1126 0.0370 1 9.27 0.0023

Za 0.1619 0.0384 1 17.8 <.0001 0.1662 0.0376 1 19.6 <.0001

Zr-0.0615 0.0438 1 1.97 0.16

Z5-0.0725 0.0553 1 1.72 0.19

Z9 0.1064 0.0384 1 7.69 0.0055 0.1072 0.0376 1 8.14 0.0043

ZZee -0.1380 0.0739 1 3.48 0.062

ZZ55 -0.0143 0.0553 1 0.0700 0.80

ZZea 0.0210 0.0375 1 0.31 0.58

ZZer -0.0272 0.0383 1 0.50 0.48

ZZe5 -0.1109 0.0795 1 1.95 0.16

ZZe9 -0.0135 0.0377 1 0.13 0.72

0.7827

1.1294 1.1337

1

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

1 2

veh

2


4

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 FM41FM5 FM6 FM7 FM8 FM9 FM10 FM11 FM12

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 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

FM1225 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.
5

PM (Bag 2): Coefficients and Tests of Effect for the Full and Reduced Models, with respect to the 

17-term extended model.

Effect Full Model Reduced Model (FM12)

Estimate Std. Err. d.f. χ

2

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

2

- value Pr>χ2

Intercept1

Ze 0.0019 0.0679 1 0.0000 0.98 0.1158 0.0450 1.0000 6.6300 0.0100

Za 0.2522 0.0461 1 30.0 <0.0001 0.1988 0.0398 1.0000 24.9000 <0.0001

Zr-0.1588 0.0630 1 6.35 0.012

Z5-0.1865 0.0903 1 4.26 0.039 -0.0037 0.0463 1.0000 0.0100 0.9355

Z9 0.1566 0.0494 1 10.1 0.0015 0.0953 0.0377 1.0000 6.3900 0.0115

ZZee -0.1590 0.0770 1 4.27 0.039

ZZ55 -0.0315 0.0629 1 0.25 0.62

ZZea -0.0078 0.0625 1 0.020 0.90

ZZer -0.0249 0.0423 1 0.35 0.56

ZZe5 -0.1421 0.0814 1 3.05 0.081

ZZe9 0.1097 0.0515 1 4.53 0.033

ZZar -0.1059 0.0788 1 1.81 0.18

ZZa5 -0.1157 0.0849 1 1.86 0.17

ZZa9 0.0346 0.0430 1 0.65 0.42

ZZ59 0.1600 0.0560 1 8.16 0.0043 0.1059 0.0402 1.0000 6.9500 0.0084

ZZr9 -0.0118 0.0487 1 0.060 0.81

1.1194 1.1295

1

 Not fit by Tobit model.

1 2

veh

2

