### 1

**Assessing	the	Effect	of	Five	Gasoline	Properties	on	Exhaust	Emissions	from	Light**

 

** Duty	Vehicles	certified	to	Tier**

**- 2	Standards** 
**Analysis of	Data	from	EPA	Phase	3** 

**(EPAct/V2/E**

**- 89)** 



## Appendix **I.2d**

**Final	Model	Fitting**

**Non**

**- Methane	Organic	Gases**  **( NM**  **O G**  **)	( Bag	1**  **)**

No. Observations: 956

No. Vehicles: 1 5

No. censored measurements: 0 No. missing measurements: 0

No. measurements removed: 0 Model Ty pe: Mixed model

### 2



## I.2d **.1			Model	fitting	with	respect	to	the	11**

**- term	design	model.** 

**Design Model (11**

**- terms):**  **Bayesian Information Criterion (BIC) vs. number of terms in model (**  **p )**  **for all possible models respecting hierarchy.**

**Design Model (11**

**- terms):**  **Bayesian Information Criterion (BIC) vs. number of terms in model (**  **p )**  **for all possible models respecting hierarchy (CLOSEUP of previous figure).**

### 3

**Design Model (11**

**- terms):**  **Bayesian Information Criterion (BIC) vs. number of terms in model (**  **p )**  **for all possible models respecting hierarchy (CLOSEUP of previous figure).**

### 4

**NMOG (**  **Bag 1 ): Number of terms (**  **p ), Goodness** 

**- of** 

**- fit (BIC) and terms included in the 35 best** 

**** **fitting candidate models (out of a total of 294 possible models with hierarchy). (Terms included in models ranked 1** 

**- 8**  **co mprise the “superset” for fin**  **al model**

**- fitting).** 

**Rank p**  **BI**

**C**etOHAromRVPT50T90etOH×etOHT50×T50etOH×ArometOH×RVPetOH×T50etOH×T90

1 11 346.525 

### • • • • • • • • • • 2 10 347.069 

### • • • • • • • • • 3 8 347.64 

### • • • • • • • 4 9 347.871 

### • • • • • • • • 5 9 348.234 

### • • • • • • • • 6 10 348.532 

### • • • • • • • • • 7 8 348.624 

### • • • • • • • 8 6 348.746 

### • • • • •

9 12 349.101 

### • • • • • • • • • • • 10 7 349.135 

### • • • • • • 11 9 349.202 

### • • • • • • • • 12 7 349.698 

### • • • • • • 13 9 349.712 

### • • • • • • • • 14 11 349.733 

### • • • • • • • • • • 15 10 349.944 

### • • • • • • • • • 16 9 350.005 

### • • • • • • • • 17 10 350.101 

### • • • • • • • • • 18 8 350.178 

### • • • • • • • 19 9 350.301 

### • • • • • • • • 20 10 350.607 

### • • • • • • • • • 21 11 350.763 

### • • • • • • • • • • 22 9 350.914 

### • • • • • • • • 23 10 350.925 

### • • • • • • • • • 24 7 350.96 

### • • • • • • 25 7 351.056 

### • • • • • • 26 8 351.155 

### • • • • • • • 27 7 351.404 

### • • • • • • 28 8 351.455 

### • • • • • • • 29 10 351.619 

### • • • • • • • • • 30 8 351.751 

### • • • • • • • 31 8 351.87 

### • • • • • • • 32 8 351.992 

### • • • • • • • 33 9 352.154 

### • • • • • • • • 34 8 352.393 

### • • • • • • • 35 10 352.393 

### • • • • • • • • • **De si**  **gn T**  **erm s** 

### 5 **Models fit for NMOG**  **( Bag 1**  **): (all models include an intercept term).**

Model Term Notation Model Superset SM2 1


### etOH Z

e ● ● 

### Arom Z

a ● ● 

### RVP Z

r ● ● 

### T50 Z

5 ● ● 

### T90 Z

9 ● 

### × etOH × etOH ZZ ee ● ● 

### T50 × T50 ZZ 55 ● ● 

### etOH × Arom ZZ ea ● ● 

### etOH × RVP ZZ er --- --- 

### etOH × T50 ZZ e5 ● ● 

### etOH × T90 ZZ e9 ● 

### × 1 denotes “Superset minus 2

. ”



### NMOG **( Bag 1**  **): Model fitting history, starting with the 10** 

**- term superset model.** 



### Fit Parameters Test with respect to Previous Model 

### Model p - 2 ln

L BI C 1 

### Dev. d Pr> χ 2


### Superset 2 

### 11 311.321 346.525 SM2 9 318.083 347.871 6.762 2 0.034

1 A lower value indicates a better fit. 2 Best fit with respect to the 11

- term design model.

### 6

**NMOG (**  **Bag 1 ):**  **Co efficients and**  **Tests of Effect for the Superset and Reduced Models, with respect to the 1**  **1**

**- term**  **design model.** 
Effect Superset Model Reduced Model (Superset)

Estimate Std.Err. d.f. t

- value Pr> t Estimate Std.Err. d.f. t

- value Pr> t 

### Intercept

- 0.9520 0.09077 15

- 10.49 <0.0001 

### Z e 0.07981 0.01326 941 6.02 <0.0001 

### Z a 0.08789 0.00929 941 9.46 <0.0001 

### Z r - 0.04595 0.01053 941

- 4.36 <0.0001 

### Z 5 0.1344 0.01329 941 10.12 <0.0001 

### Z 9 0.01593 0.00925 941 1.72 0.0855 Reduced Model = Superset Model 

### ZZ ee 0.04594 0.01760 941 2.61 0.00918 

### ZZ 55 0.07680 0.01336 941 5.75 <0.0001 

### ZZ ea 0.01635 0.00906 941 1.80 0.0714 

### ZZ er - - - - - 

### ZZ e5 0.04754 0.01893 941 2.51 0.0122 

### ZZ e9 0.01961 0.00902 941 2.17 0.0300

2 veh 

###  0.1224
2

 

###  0.07538

### 7



## I.2d **.2 Model	Fitting	with	respect	to	the	16** 

**- term	extended	Model.** 

**E xtended Model (16** 

**- terms)**  **: Bayesian Information Criterion (BIC) vs. number of terms in model**  **( p**  **) for all possible models respecting hierarchy.**

**Extended Model (16**

**- terms)**  **: Bayesian Information Criterion (BIC) vs. number of terms in model (**  **p ) for subset of models respecting hierarchy (CLOSEUP**  **of previous figure**  **)**

**.**

### 8

**Extended Model (16**

**- terms): Bayesian Information Criterion (BIC) vs. number of terms in model**  **( p**  **) for subset of models respecting hierarchy (CLOSEUP of previous figure).**

### 9

**NMOG (**  **Bag 1 ): Number of terms (**  **p ), Goodness** 

**- of** 

**- fit (BIC) and**  **terms included in the 35 best**

  ** fitting candidate models (out of a total of 2** **, 9**  **6 4 possible models with hierarchy). (Terms included in**  **models ranked 1**

**- 8**  **co mprise the “superset” for final model** 

**- fitting).** 

**Rank p**  **BI**

**C**etOHAromRVPT50T90etOH×etOHT50×T50etOH×ArometOH×RVPetOH×T50etOH×T90Arom×RVPArom×T50Arom×T90T50×T90RVP×T90

1 14 328.80 • • • • • • • • • • • • • 2 12 329.14 • • • • • • • • • • • 3 13 329.58 • • • • • • • • • • • • 4 15 329.62 • • • • • • • • • • • • • • 5 11 330.02 • • • • • • • • • • 6 13 330.32 • • • • • • • • • • • • 7 12 330.33 • • • • • • • • • • • 8 15 330.35 • • • • • • • • • • • • • •

9 11 330.54 • • • • • • • • • • 10 15 330.60 • • • • • • • • • • • • • • 11 13 330.73 • • • • • • • • • • • • 12 10 330.77 • • • • • • • • • 13 13 330.86 • • • • • • • • • • • • 14 14 330.87 • • • • • • • • • • • • • 15 11 330.87 • • • • • • • • • • 16 14 330.90 • • • • • • • • • • • • • 17 14 331.03 • • • • • • • • • • • • • 18 13 331.38 • • • • • • • • • • • • 19 16 331.41 • • • • • • • • • • • • • • • 20 11 331.42 • • • • • • • • • • 21 13 331.45 • • • • • • • • • • • • 22 10 331.52 • • • • • • • • • 23 14 331.52 • • • • • • • • • • • • • 24 12 331.56 • • • • • • • • • • • 25 13 331.61 • • • • • • • • • • • • 26 13 331.66 • • • • • • • • • • • • 27 12 331.69 • • • • • • • • • • • 28 13 331.75 • • • • • • • • • • • • 29 13 331.80 • • • • • • • • • • • • 30 12 331.83 • • • • • • • • • • • 31 12 331.83 • • • • • • • • • • • 32 16 331.87 • • • • • • • • • • • • • • • 33 14 331.89 • • • • • • • • • • • • • 34 16 332.06 • • • • • • • • • • • • • • • 35 9 332.34 • • • • • • • • **De si**  **gn T**  **erm s**  **Ex te**  **nd ed**  **T erm**  **s**

### 10 **Models fit for NMOG**  **( Bag 1**  **): (all models include an intercept term).** 

Model Term Notation Model Superset SM3 1 

### SM7 etOH Z

e ● ● ● 

### Arom Z

a ● ● ● 

### RVP Z

r ● ● ● 

### T50 Z

5 ● ● ● 

### T90 Z

9 ● ● 

### × etOH × etOH ZZ ee ● ● ● 

### T50 × T50 ZZ 55 ● ● ● 

### etOH × Arom ZZ ea ● ● ● 

### etOH × RVP ZZ er ● 

### × etOH × T50 ZZ e5 ● ● ● 

### etOH × T90 ZZ e9 ● ● 

### ×

Arom × RVP ZZ ar ● ● ● 

### Arom × T50 ZZ a5 ● 

### × Arom × T90 ZZ a9 ● ● 

### × T50 × T90 ZZ 59 ● ● 

### × RVP × T90 ZZ r9 ● 

### ×

1 denotes “Superset minus 3, etc. ”



### NMOG **( Bag 1**  **): Model fitting history, starting with the 9** 

**- term superset**  **model.**



### Fit Parameters Test with respect to Previous Model 

### Model p - 2 ln

L BI C 1 

### Dev. d Pr> χ 2


### Superset 17 282.156 333.609 SM 3 2 

### 14 285.473 328.802 3.317 3 0.345 SM7 10 313.769 346.266 28.296 4 0.000011

1 A lower value indicates a better fit. 2 Best fit with respect to the 16

- term extended model.

### 11

**NMOG (**  **Bag 1 ):**  **Co efficients and Tests of Effect for the Superset and Reduced Models, with respect**  **to the 1 6** 

**- term**  **extended model.** 

Effec t Fu ll Model ( superset ) Re duced Model ( SM3)
Es ti ma te St d. E

rr. d. f. t -v al

ue Pr> t Es ti

ma te St d. E

rr. d. f. t -v al

ue Pr> t In ter cep t -0.9508 0. 09047 15 -10.5 0.00000 -0.9513 0.09042 15 -10.5 0.00000
Z e 0.1054 0. 01586 941 6.65 0.00000 0.0927 0.01406 941 6.60 0.00000
Z a 0.1072 0. 00995 941 10.8 0.00000 0.1051 0.00988 941 10.6 0.00000
Z r -0.03611 0. 01339 941 -2.70 0.0071 -0.0483 0.01064 941 -4.54 0.00001
Z 5 0.1696 0. 01767 941 9.60 0.00000 0.1541 0.01514 941 10.2 0.00000
Z 9 0.01217 0. 01025 941 1.19 0.24 0.0112 0.00961 941 1.17 0.24
ZZ ee 0.05186 0. 01849 941 2.80 0.0051 0.0420 0.01756 941 2.39 0.017
ZZ 55 0.08968 0. 01508 941 5.94 0.00000 0.0787 0.01360 941 5.78 0.00000
ZZ ea 0.03775 0. 01496 941 2.52 0. 012 0.0217 0.00918 941 2.36 0.018
ZZ er 0.00726 0. 01014 941 0.72 0.47
ZZ e5 0.04249 0. 01953 941 2.18 0. 030 0.0357 0.01914 941 1.87 0.062
ZZ e9 0.04148 0. 01199 941 3.46 0.00056 0.0476 0.01098 941 4.34 0.00002

ZZ ar 0.04390 0. 01620 941 2.71 0.0069 0.0272 0.01263 941 2.16 0.031
ZZ a5 0.01941 0. 01806 941 1.07 0.28
ZZ a9 0.01980 0. 01014 941 1.95 0. 051 0.0205 0.00996 941 2.06 0.040
ZZ 59 0.05104 0. 01349 941 3.78 0.00016 0.0544 0.01201 941 4.53 0.00001
ZZ r9 -0.01130 0. 01146 941 -0.985 0.32

0.1216 0.1215

0.07309 0.07335 2

ve h 

### 

2

 

###  2

ve h 

### 

2

 

### 