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**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.4n Final	Model	Fitting**  **Methane (C**  **H 4**  

## )	( **Bag	2 )** 

No. Observations: 956 No. Vehicles: 15 No. censored measurements: 0 No. missing measurements: 0 No. measurements removed: 0 Model Ty pe: Mixed model

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## I.4n **.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

**CH 4**  

### ( **Bag 2 ): 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** 
**- 6**  **comprise the “superset” for final model** 
**- fitting).** 

### 5 **Models fit for CH**  **4** 

### ( **Bag 2 ): (all models include an intercept term).** 

Model Term Notation Model Superset SM 2 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 Represents “Superset minus 2,” etc.



### CH4 **( Bag 2**  **): 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 10

- 691.760

- 659.263 SM1 2 

### 8

- 687.712

- 660.632 4.048 2 0.132

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

- term extended model.

### 6

**CH 4**  

### ( **Bag 2 ): Coefficients and Tests**  **of Effect for the Superset and Reduced Models, with respect to**  **the 1 1** 
**- term**  **design model.** 


### Effe ct Fu ll Model (su perset ) Re duced Model (S M2) 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 tercept -5.7080 0. 2722 15 -21.0 0.000000 -5.7075 0.2722 15 -21.0 0.000000 Z e 0. 05859 0. 006829 941 8. 58 0.000000 0.05860 0.006839 941 8. 57 0.000000 Z a -0.09846 0. 005308 941 -18.5 0.000000 -0.09836 0.005317 941 -18.5 0.000000 Z r -0.02053 0. 006080 941 -3.38 0. 00076 -0.02049 0.006036 941 -3.39 0. 00072 Z 5 0. 04321 0. 007399 941 5. 84 0.000000 0.04394 0.007393 941 5. 94 0.000000 Z 9 0. 02539 0. 005359 941 4. 74 0.000002 0.02575 0.005290 941 4. 87 0.000001 ZZ ee --- --- --- --- --- --- --- --- --- --- ZZ 55 0. 01248 0. 005381 941 2. 32 0. 021 0.01227 0.005379 941 2. 28 0. 023 ZZ ea 0.008520 0. 005183 941 1. 64 0.10 0. 008769 0.005185 941 1. 69 0. 091 ZZ er -0.007004 0. 005258 941 -1.33 0.18 ZZ e5 --- --- --- --- --- --- --- --- --- --- ZZ e9 -0.006794 0. 005260 941 -1.29 0.20

1.1109 1.1108 0. 02507 0. 02518 2 ve h 

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2  

###  2 veh 

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2  

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## I.4n **.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

**CH 4**  

### ( **Bag 2 ): 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** 
**- 5**  **comprise the “superset” for final model**
**- fitting).** 

**Rank p**  **BI**

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

1 10 -6 67. 041 

### • • • • • • • • • 2 9 -6 66. 822 

### • • • • • • • • 3 8 -6 66. 263 

### • • • • • • • 4 9 -6 65. 701 

### • • • • • • • • 5 11 -6 65. 585 

### • • • • • • • • • •
6 11 -6 65. 274 

### • • • • • • • • • • 7 11 -6 65. 265 

### • • • • • • • • • • 8 10 -6 65. 124 

### • • • • • • • • • 9 11 -6 65. 117 

### • • • • • • • • • • 10 10 -6 65. 026 

### • • • • • • • • • 11 10 -6 65. 024 

### • • • • • • • • • 12 9 -6 65. 023 

### • • • • • • • • 13 10 -664.96 

### • • • • • • • • • 14 11 -6 64. 827 

### • • • • • • • • • • 15 9 -6 64. 797 

### • • • • • • • • 16 11 -6 64. 614 

### • • • • • • • • • • 17 8 -6 64. 601 

### • • • • • • • 18 11 -6 64. 568 

### • • • • • • • • • • 19 10 -6 64. 563 

### • • • • • • • • • 20 10 -6 64. 543 

### • • • • • • • • • 21 10 -6 64. 491 

### • • • • • • • • • 22 11 -6 64. 448 

### • • • • • • • • • • 23 12 -6 64. 436 

### • • • • • • • • • • • 24 9 -6 64. 377 

### • • • • • • • • 25 9 -6 64. 302 

### • • • • • • • • 26 10 -6 64. 246 

### • • • • • • • • • 27 12 -6 64. 207 

### • • • • • • • • • • • 28 8 -664.16 

### • • • • • • • 29 10 -6 64. 151 

### • • • • • • • • • 30 10 -6 64. 114 

### • • • • • • • • • 31 10 -6 64. 016 

### • • • • • • • • • 32 11 -6 63. 984 

### • • • • • • • • • • 33 9 -6 63. 976 

### • • • • • • • • 34 10 -6 63. 884 

### • • • • • • • • • 35 12 -6 63. 861 

### • • • • • • • • • • • **De si**  **gn T** **erm s**  **Ex te**  **nd ed**  **Te rm** **s**

### 10 **Models fit for CH**  **4** 

### ( **Bag 2 ): (all models include an intercept term).** 

Model T erm Notation Model Superset SM 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 

### --- --- Arom × RVP ZZ ar 

### --- --- Arom × T50 ZZ a5 

### --- --- Arom × T90 ZZ a9 

### --- --- T50 × T90 ZZ 59 ● ● 

### RVP × T90 ZZ r9 ● ●
1 Denotes “Superset minus 1,” etc.



### CH **4** 

### ( **Bag 2 ): Model fitting history, starting with the 15** 
**- 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 11

- 700.789

- 665.585 SM 1 2 

### 10

- 699.537

- 667.041 1.252 1 0.263

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

- term extended model.

### 11

**CH 4**  

### ( **Bag 2 ): Coefficients and Tests of Effect for the Superset and Reduced Models, with respect to**  **the 1 6** 
**- term**  **extended model.** 


### Effe ct Fu ll Model (su perset ) Re duced Model (S M1) 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 tercept -5.7078 0. 2722 15 -21.0 0.000000 -5.7076 0.2722 15 -21.0 0.000000 Z e 0. 06063 0. 006873 941 8. 82 0.000000 0.06076 0.006877 941 8. 84 0.000000 Z a -0.09260 0. 005608 941 -16.5 0.000000 -0.09211 0.005595 941 -16.5 0.000000 Z r -0.02135 0. 006033 941 -3.54 0. 00042 -0.02082 0.006018 941 -3.46 0. 00056 Z 5 0. 04424 0. 007413 941 5. 97 0.000000 0.04477 0.007403 941 6. 05 0.000000 Z 9 0. 02510 0. 005324 941 4. 71 0.000003 0.02445 0.005295 941 4. 62 0.000004 ZZ ee --- --- --- --- --- --- --- --- --- --- ZZ 55 0. 01445 0. 005496 941 2. 63 0.0087 0.01398 0.005483 941 2. 55 0. 011 ZZ ea 0. 01015 0. 005202 941 1. 95 0. 051 0.01047 0.005198 941 2. 01 0. 044 ZZ er -0.005907 0. 005277 941 -1.12 0.26 ZZ e5 --- --- --- --- --- --- --- --- --- --- ZZ e9 --- --- --- --- --- --- --- --- --- --- ZZ ar --- --- --- --- --- --- --- --- --- --- ZZ a5 --- --- --- --- --- --- --- --- --- --- ZZ a9 --- --- --- --- --- --- --- --- --- --- ZZ 59 0. 01241 0. 005994 941 2. 07 0. 039 0.01374 0.005879 941 2. 34 0. 020 ZZ r9 -0.01034 0. 005802 941 -1.78 0. 075 -0.009921 0.005794 941 -1.71 0. 087

1. 111 1.1109 0. 02483 0. 02486 2 ve h 

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2  

###  2 veh 

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2  

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