Assessing	the	Effect	of	Five	Gasoline	Properties	on	Exhaust	Emissions	from	LightDuty	Vehicles	certified	to	Tier-2	Standards

(EPAct/V2/E-89:	Phase	3)

Part	II:		Data	Analysis	and	Model	Development

APPENDIX		E

Preliminary	Reduced	Models
Development of the models presented below is described in Section 5.3 of the report. All models 

are based on the 16-parameter full model, as shown in Equation 1. All terms were included at 

the outset of model fitting, with the exception of T90×T90. Using the notation for standardized 

predictors, also shown in Equation 2, the model is also expressed in Equation 2. Table E.1 

summarizes the model-fitting approaches applied to each bag for each emission. Table E.2 

through E.7 present the coefficients for interim reduced models for THC, NMOG, CH4, CO, 

NOx and PM, respectively. 



    

   

 

    



              

           

  

         

 

Arom T50 Arom T90 T50 T90 Arom RVP RVP T90

etOH Arom etOH RVP etOH T50 etOH T90

T50 etOH

etOH Arom RVP T50 T90

ln

12 13 14 15 16

8 9 10 11

2

7

2

6

1 2 3 4 5

Y 0

Equation	

1



    

   

 

    



    

   



    

 

12 5 13 9 14 59 15 16 9

8 9 10 5 11 9

6 55 7

1 2 3 4 5 5 9

0

ln

a a ar r

ea er e e

ee

e a r

ZZ ZZ ZZ ZZ ZZ

ZZ ZZ ZZ ZZ

ZZ ZZ

Z Z Z Z Z

Y

Equation	2
Table	E.1.		Design and	Modeling	Parameters	for	Best-fit	models,	by	Compound	and	Bag.	

Compound Bag nremoved Model Type Selection Method

THC 1 0 Mixed Minimize BIC

2 0 Mixed Minimize BIC

3 0 Mixed Minimize BIC

CO 1 0 Mixed Minimize BIC

2 0 Mixed Minimize BIC

3 0 Mixed Minimize BIC

NOx 1 0 Mixed Minimize BIC

2 0 Mixed Minimize BIC

3 0 Tobit Backwards elimination

PM 1 2 Tobit Backwards elimination

2 1 Tobit Backwards elimination

3 1 Tobit Backwards elimination

NMOG 1 0 Mixed Minimize BIC

2 0 Tobit Backwards elimination

3 0 Tobit Backwards elimination

CH4 1 0 Mixed Backwards elimination

2 0 Mixed Backwards elimination

3 0 Mixed Backwards elimination
Table	E.2.		 THC:		Reduced	Models,	starting	from	16-term	full	model.

Model term Notation Bag 1 Bag 2 Bag 3

Intercept Intercept -0.8658 -4.9092 -4.2300

etOH Ze

0.06793 0.06814 0.007879

Arom Za

0.08343 -0.02281 -0.06120

RVP Zr

-0.04669 -0.01423

T50 Z5

0.1490 -0.03953 0.03595

T90 Z9

0.01435 0.07154 0.04904

etOH × etOH ZZee

0.04065 0.06681

T50 × T50 ZZ55 0.07555

etOH × Arom ZZea

0.02297 0.03054

etOH × RVP ZZer

0.01666

etOH × T50 ZZe5 0.03426 0.04028 -0.03125

etOH × T90 ZZe9 0.04782

Arom × RVP ZZar

Arom × T50 ZZa5 0.03386

Arom × T90 ZZa9 0.02264

T50 × T90 ZZ59 0.02886

RVP × T90 ZZr9

Table	E.3.		NMOG:		Reduced	Models,	starting	from	16-term	full	model.

Model term Notation Bag 1 Bag 2 Bag 3

Intercept Intercept 0.9513 -5.51661-5.84491

etOH Ze 0.09272 0.0730 0.0339

Arom Za 0.1051 0.0355

RVP Zr-0.04834 -0.0463 -0.0572

T50 Z5 0.1541 0.0859 0.0783

T90 Z9 0.01124 0.1091 0.1467

etOH × etOH ZZee 0.04204 -0.0424

T50 × T50 ZZ55 0.07866 0.0412

etOH × Arom ZZea 0.02171 0.0718

etOH × RVP ZZer -0.0313 0.0707

etOH × T50 ZZe5 0.03576 -0.0728

etOH × T90 ZZe9 0.04763

Arom × RVP ZZar 0.02724

Arom × T50 ZZa5 0.0738

Arom × T90 ZZa9 0.02049 0.0327

T50 × T90 ZZ59 0.05437 0.0293

RVP × T90 ZZr9

1 Not fit by Tobit model; calculated manually from intercepts for individual vehicles.
Table	E.4.		CH4:		Reduced	Models,	starting	from	16-term	full	model.

Model term Notation Bag 1 Bag 2 Bag 3

Intercept Intercept -3.0068 -5.7076 -4.5979

etOH Ze 0.08877 0.06076 0.03187

Arom Za-0.09816 -0.09211 -0.1004

RVP Zr-0.02455 -0.02082

T50 Z5 0.1059 0.04477 0.01886

T90 Z9 0.008573 0.02445 0.01856

etOH × etOH ZZee 0.03133

T50 × T50 ZZ55 0.05882 0.01398

etOH × Arom ZZea 0.03977 0.01047

etOH × RVP ZZer

etOH × T50 ZZe5 0.02883 -0.02007

etOH × T90 ZZe9 0.02655

Arom × RVP ZZar 0.02791

Arom × T50 ZZa5 0.02585

Arom × T90 ZZa9 0.03072

T50 × T90 ZZ59 0.0228 0.01374

RVP × T90 ZZr9 -0.00992

Table	E.5.		 CO:	Reduced	Models,	starting	from	16-term	full	model.

Model term Notation Bag 1 Bag 2 Bag 3

Intercept Intercept 1.3472 -1.3896 -1.1409

etOH Ze -0.06967 -0.08154

Arom Za -0.01156 0.09798 0.07191

RVP Zr 0.02063 0.02838 0.02393

T50 Z5 0.02159 0.02486

T90 Z9 -0.1469 0.04180 0.05781

etOH × etOH ZZee 0.08535

T50 × T50 ZZ55 0.07222

etOH × Arom ZZea 0.06244

etOH × RVP ZZer

etOH × T50 ZZe5 0.1117

etOH × T90 ZZe9

Arom × RVP ZZar

Arom × T50 ZZa5

Arom × T90 ZZa9 0.03861

T50 × T90 ZZ59 0.02177

RVP × T90 ZZr9
Table	E.6.		NOx:	Reduced	Models,	starting	from	16-term	full	model.

Model term Notation Bag 1 Bag 2 Bag 3

Intercept Intercept -3.01636 -4.7882 -5.2554

etOH Ze 0.03802 0.04112 0.0884

Arom Za 0.1336 0.03534 0.0667

RVP Zr -0.01418 -0.01464 0.169

T50 Z5 0.01026 -0.0224

T90 Z9 0.02389 -0.0004567 0.085

etOH × etOH ZZee -0.05980

T50 × T50 ZZ55 -0.05701

etOH × Arom ZZea -0.03038 0.02739

etOH × RVP ZZer

etOH × T50 ZZe5 -0.9774 0.0637

etOH × T90 ZZe9 0.02544

Arom × RVP ZZar

Arom × T50 ZZa5 0.0894

Arom × T90 ZZa9 -0.04769

T50 × T90 ZZ59

RVP × T90 ZZr9 0.04562 -0.04014

Table	E.7.			PM:	Reduced	models,	starting	from	16-term	full	model.

Model term Notation Bag 1 Bag 2 Bag 3

Intercept

etOH Ze

0.1640 0.1158 -0.02120

Arom Za

0.3795 0.1988 0.01860

RVP Zr

-0.1275

T50 Z5

0.06650 -0.00370 -0.04110

T90 Z9

0.2882 0.09530

etOH × etOH ZZee

T50 × T50 ZZ55 0.08560

etOH × Arom ZZea

0.08490

etOH × RVP ZZer

etOH × T50 ZZe5 -0.08240

etOH × T90 ZZe9

Arom × RVP ZZar

-0.1062

Arom × T50 ZZa5

Arom × T90 ZZa9

T50 × T90 ZZ59 0.1059

RVP × T90 ZZr9