### 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.3d**
**Final	Model	Fitting**
**Non**
**- Methane**  **Hydrocarbons (**  **NMHC )	(**  **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.3d **.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

**NMHC (**  **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** 

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

**- fitting).** 

**Rank p**  **BI**

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

1 11 357.702 

### • • • • • • • • • • 2 9 359.339 

### • • • • • • • • 3 10 360.017 

### • • • • • • • • • 4 8 360.223 

### • • • • • • • 5 12 360.243 

### • • • • • • • • • • •

6 10 361.141 

### • • • • • • • • • 7 10 361.761 

### • • • • • • • • • 8 10 362.04 

### • • • • • • • • • 9 10 362.209 

### • • • • • • • • • 10 9 362.298 

### • • • • • • • • 11 9 362.635 

### • • • • • • • • 12 11 362.678 

### • • • • • • • • • • 13 9 362.892 

### • • • • • • • • 14 9 363.339 

### • • • • • • • • 15 6 363.737 

### • • • • • 16 8 363.753 

### • • • • • • • 17 11 363.849 

### • • • • • • • • • • 18 11 364.257 

### • • • • • • • • • • 19 7 364.352 

### • • • • • • 20 11 364.464 

### • • • • • • • • • • 21 5 364.584 

### • • • • 22 9 364.705 

### • • • • • • • • 23 7 364.811 

### • • • • • • 24 10 364.985 

### • • • • • • • • • 25 10 365.131 

### • • • • • • • • • 26 10 365.31 

### • • • • • • • • • 27 6 365.57 

### • • • • • 28 9 365.696 

### • • • • • • • • 29 8 365.966 

### • • • • • • • 30 9 366.096 

### • • • • • • • • 31 8 366.36 

### • • • • • • • 32 9 366.361 

### • • • • • • • • 33 8 366.716 

### • • • • • • • 34 8 366.841 

### • • • • • • • 35 8 367.009 

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

**s**

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

Model Term Notation Model Superset SM 1 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 1. ”



### NMHC **( 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 12 322.331 360.243 SM2 2 

### 11 322.497 357.702 0.167 1 0.683

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

- term design model.

### 6

**NMHC (**  **Bag 1 ):**  **Co efficients 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 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 ter cept -1.0314 0.09233 15 -11.2 0. 00000 -1.0315 0. 09231 15 -11.2 0. 00000 Z e 0. 03153 0.01341 941 2. 35 0. 019 0.03094 0. 01333 941 2. 32 0. 02054 Z a 0. 09476 0.00935 941 10.1 0. 00000 0.09461 0. 00934 941 10.1 0. 00000 Z r -0.04514 0.01068 941 -4.23 0.000026 -0.04568 0. 01059 941 -4.31 0.000018 Z 5 0.1376 0.01347 941 10.22 0. 00000 0.13689 0. 01336 941 10.25 0. 00000 Z 9 0. 02123 0.00935 941 2. 27 0. 023 0.02160 0. 00931 941 2. 32 0. 021 ZZ ee 0. 04746 0.01800 941 2. 64 0.0085 0.04612 0. 01770 941 2. 61 0.0093 ZZ 55 0. 07579 0.01348 941 5. 62 0. 00000 0.07534 0. 01343 941 5. 61 0. 00000 ZZ ea 0. 02076 0.00914 941 2. 27 0. 023 0.02045 0. 00911 941 2. 24 0. 025 ZZ er 0. 00381 0.00933 941 0.408 0.68 ZZ e5 0. 04862 0.01932 941 2. 52 0. 012 0.04729 0. 01904 941 2. 48 0. 013 ZZ e9 0. 02384 0.00918 941 2. 60 0.0095 0.02441 0. 00907 941 2. 69 0.0072

0.1267 0.1266
0. 07623 0. 07624 2 ve h 

### 
2  

###  2 veh 

### 
2  

### 

### 7



## I.3d **.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

**NMHC (**  **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 14 341.37 • • • • • • • • • • • • • 2 12 341.85 • • • • • • • • • • • 3 15 342.09 • • • • • • • • • • • • • • 4 13 342.11 • • • • • • • • • • • • 5 11 342.77 • • • • • • • • • • 6 15 342.83 • • • • • • • • • • • • • • 7 12 342.89 • • • • • • • • • • • 8 13 342.92 • • • • • • • • • • • •

9 15 343.19 • • • • • • • • • • • • • • 10 14 343.31 • • • • • • • • • • • • • 11 14 343.39 • • • • • • • • • • • • • 12 13 343.51 • • • • • • • • • • • • 13 14 343.52 • • • • • • • • • • • • • 14 13 343.57 • • • • • • • • • • • • 15 11 343.78 • • • • • • • • • • 16 13 343.85 • • • • • • • • • • • • 17 16 343.90 • • • • • • • • • • • • • • • 18 14 343.99 • • • • • • • • • • • • • 19 13 344.08 • • • • • • • • • • • • 20 13 344.13 • • • • • • • • • • • • 21 12 344.24 • • • • • • • • • • • 22 16 344.30 • • • • • • • • • • • • • • • 23 14 344.43 • • • • • • • • • • • • • 24 13 344.48 • • • • • • • • • • • • 25 13 344.49 • • • • • • • • • • • • 26 12 344.52 • • • • • • • • • • • 27 16 344.57 • • • • • • • • • • • • • • • 28 11 345.02 • • • • • • • • • • 29 15 345.05 • • • • • • • • • • • • • • 30 14 345.12 • • • • • • • • • • • • • 31 11 345.21 • • • • • • • • • • 32 10 345.28 • • • • • • • • • 33 12 345.31 • • • • • • • • • • • 34 13 345.40 • • • • • • • • • • • • 35 10 345.44 • • • • • • • • • **De si**  **gn Te**  **rm s**  **Ex te**  **nd ed**  **T erm**  **s**

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

Mod el 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 ● ●


### Arom × RVP ZZ ar ● ● 

### Arom × T50 ZZ a5 ● 

### × Arom × T90 ZZ a9 ● ● 

### T50 × T90 ZZ 59 ● ● 

### RVP × T90 ZZ r9 

### --- ---

1 Represents “Superset minus 2,” etc.



### NMHC **( 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 16 295.558 344.303 SM 2 2 

### 14 298.043 341.372 2.485 2 0.289

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

- term extended model.

### 11

**NMHC (**  **Bag 1 ):**  **Co efficients**  **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 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 ter cept -1.0304 0.09200 15 -11.2 0. 00000 -1.0308 0. 09197 15 -11.2 0. 00000 Z e 0. 05238 0.01514 941 3. 46 0. 00057 0.04439 0. 01415 941 3. 14 0.0018 Z a 0.1125 0.00998 941 11.3 0. 00000 0.11119 0. 00994 941 11.2 0. 00000 Z r -0.03708 0.01333 941 -2.78 0.0055 -0.04765 0. 01070 941 -4.45 0.000010 Z 5 0.1683 0.01710 941 9. 84 0. 00000 0.15733 0. 01524 941 10.3 0. 00000 Z 9 0. 01811 0.01032 941 1. 76 0. 079 0.01682 0. 00967 941 1. 74 0. 082 ZZ ee 0. 04814 0.01801 941 2. 67 0.0076 0.04274 0. 01768 941 2. 42 0. 016 ZZ 55 0. 08384 0.01428 941 5. 87 0. 00000 0.07769 0. 01369 941 5. 68 0. 00000 ZZ ea 0. 04042 0.01492 941 2. 71 0.0069 0.02594 0. 00924 941 2. 81 0.0051 ZZ er 0. 00718 0.01020 941 0.703 0.48 ZZ e5 0. 03943 0.01938 941 2. 03 0. 042 0.03579 0. 01926 941 1. 86 0. 063 ZZ e9 0. 04967 0.01110 941 4. 47 0. 00001 0.05125 0. 01105 941 4. 64 0. 00000
ZZ ar 0. 04215 0.01599 941 2. 64 0. 00854 0.02820 0. 01272 941 2. 22 0. 027 ZZ a5 0. 02025 0.01818 941 1. 11 0. 26569 ZZ a9 0. 01889 0.01016 941 1. 86 0. 06315 0.02068 0. 01002 941 2. 06 0. 039 ZZ 59 0. 05480 0.01223 941 4. 48 0. 00001 0.05225 0. 01209 941 4. 32 0. 00002 ZZ r9 --- --- --- --- --- --- --- --- --- ---

0.1258 0.1257
0. 07410 0. 07430 2 ve h 

### 
2  

###  2 veh 

### 
2  

### 