## 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.2e**
**Final	Model	Fitting**
**Non**
**- Methane	Organic	Gases**  **( NM**  **O G**  **)	(Bag 2**  **)**

No. Observations: 832
No. Vehicles: 1 3 (exclude Od ys sey and Sienna)
No. censored measurements: 0 No. missing measurements: 0
No. measurements removed: 0 Model Ty pe: Mixed model

## 2



## I.2e **.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 mo dels respecting hierarchy (CLOSEUP of previous figure).** 

## 4

**NMOG (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 i ncluded in**  **models ranked 1**

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

**- fitting).** 

**Rank p**  **BI**

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



### 1 9 776.93 

### • • • • • • • • 2 8 777.286 

### • • • • • • • 3 8 777.584 

### • • • • • • • 4 6 777.605 

### • • • • • 5 10 777.832 

### • • • • • • • • • 6 9 777.881 

### • • • • • • • • 7 10 777.894 

### • • • • • • • • • 8 7 777.94 

### • • • • • •

9 9 778.301 

### • • • • • • • • 10 9 778.384 

### • • • • • • • • 11 8 778.426 

### • • • • • • • 12 9 778.57 

### • • • • • • • • 13 8 778.607 

### • • • • • • • 14 9 778.677 

### • • • • • • • • 15 9 778.785 

### • • • • • • • • 16 8 779.082 

### • • • • • • • 17 10 779.09 

### • • • • • • • • • 18 11 779.235 

### • • • • • • • • • • 19 10 779.274 

### • • • • • • • • • 20 10 779.362 

### • • • • • • • • • 21 10 779.566 

### • • • • • • • • • 22 9 779.642 

### • • • • • • • • 23 9 779.794 

### • • • • • • • • 24 10 779.909 

### • • • • • • • • • 25 9 780.024 

### • • • • • • • • 26 11 780.253 

### • • • • • • • • • • 27 10 780.321 

### • • • • • • • • • 28 11 780.336 

### • • • • • • • • • • 29 10 780.446 

### • • • • • • • • • 30 11 780.56 

### • • • • • • • • • • 31 10 780.817 

### • • • • • • • • • 32 12 781.731 

### • • • • • • • • • • • 33 11 781.927 

### • • • • • • • • • • 34 7 782.237 

### • • • • • • 35 8 782.744 

### • • • • • • • **De si**  **gn Te**  **rm s** 

## 5 **Models fit for NMOG**  **(Bag 2**  **): (all models include an intercept term).** Model Term Notation Model Superset SM2 1 

### SM5 SM4 2 

### SM3a 3 

### SM3b 4 

### 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. 2 Not nested within SM5; formed by dropping etOH × Aro m and etOH × T50 from SM2. 3 Not nested within SM5 or SM4; formed by dropping etOH × Arom from SM2. 4 Not nested within SM5, SM4 or SM3a; formed by dropping etOH × T50 from SM2.



### NMOG **(Bag 2**  **): 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 11 745.891 779.235 SM 2 2 

### 9 748.716 776.930 2.825 2 0.244 SM 5 6 757.086 777.605 8.370 3 0.0390
SM4 3 

### 7 754.855 777.940 6.140 2 0.0464
SM3a 3 

### 8 751.636 777.286 2.920 1 0.0875
SM3b 3 

### 8 751.934 777.584 3.219 1 0.0728

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

- term design model. 3 Not nested within previous model; test with respect to SM2.

## 6

**NMOG (Bag**  **2 ):**  **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 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 -5.2370 0. 2562 13 -20.4 0. 00000 -5.2360 0.2560 13 -20.4 0. 00000 Z e 

### 0. 02684 0.01675 819 1. 60 0.11 0.02673 0. 01676 819 1. 59 0. 11 Z a 

### 0. 03630 0.01306 819 2. 78 0.0056 0.03634 0. 01308 819 2. 78 0.0056 Z r 

### -0.04775 0.01489 819 -3.21 0.0014 -0.04786 0. 01475 819 -3.24 0.0012 Z 5 

### 0. 04777 0.01810 819 2. 64 0.0085 0.04915 0. 01807 819 2. 72 0.0067 Z 9 

### 0. 07197 0.01314 819 5. 48 0. 00000 0.07252 0. 01295 819 5. 60 0. 00000 ZZ ee 

### --- --- --- --- --- --- --- --- --- --- ZZ 55 

### 0. 05379 0.01451 819 3. 71 0. 00022 0.05349 0. 01452 819 3. 68 0. 00025 ZZ ea 

### 0. 02087 0.01271 819 1. 64 0.10 0.02171 0. 01269 819 1. 71 0. 088 ZZ er 

### -0.01429 0.01291 819 -1.11 0.27 ZZ e5 

### 0. 02592 0.01439 819 1. 80 0. 072 0.02586 0. 01440 819 1. 80 0. 073 ZZ e9 

### -0.01393 0.01292 819 -1.08 0.28

0.8514 0.8502
0.1306 0.1310 2
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##  2 veh 

## 
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## 

## 7



## I.2e **.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**  **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**  **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 11 775.72 • • • • • • • • • • 2 12 776.56 • • • • • • • • • • • 3 9 776.93 • • • • • • • • 4 10 777.25 • • • • • • • • • 5 8 777.29 • • • • • • •

6 12 777.49 • • • • • • • • • • • 7 11 777.50 • • • • • • • • • • 8 12 777.52 • • • • • • • • • • • 9 10 777.54 • • • • • • • • • 10 8 777.58 • • • • • • • 11 6 777.61 • • • • • 12 10 777.61 • • • • • • • • • 13 12 777.64 • • • • • • • • • • • 14 10 777.83 • • • • • • • • • 15 9 777.88 • • • • • • • • 16 10 777.89 • • • • • • • • • 17 7 777.94 • • • • • • 18 9 778.06 • • • • • • • • 19 12 778.07 • • • • • • • • • • • 20 11 778.08 • • • • • • • • • • 21 9 778.12 • • • • • • • • 22 10 778.12 • • • • • • • • • 23 13 778.16 • • • • • • • • • • • • 24 12 778.21 • • • • • • • • • • • 25 11 778.30 • • • • • • • • • • 26 9 778.30 • • • • • • • • 27 9 778.38 • • • • • • • • 28 7 778.40 • • • • • • 29 8 778.43 • • • • • • • 30 13 778.53 • • • • • • • • • • • • 31 10 778.56 • • • • • • • • • 32 9 778.57 • • • • • • • • 33 8 778.61 • • • • • • • 34 12 778.62 • • • • • • • • • • • 35 8 778.65 • • • • • • • **De si**  **gn Te**  **rm s**  **Ex te**  **nd ed**  **T erm**  **s**

## 10 **Models fit for NMOG**  **( Bag 2**  **): (all models include an intercept term).**

Model Term Notation Model Superset SM1 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. ”



### NMOG **( 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 12 740.652 776.561 SM 1 11 742.372 775.716 1.720 1 0.190

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

- term extended model.

## 11

**NMOG (**  **Bag 2 ):**  **NMOG 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 ( SM1) 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 -5.2367 0. 2562 13 -20.44 0.00000 -5.2369 0. 2561 13 -20.45 0. 00000 Z e 0. 03387 0.01709 819 1. 98 0. 048 0.02947 0. 01677 819 1. 76 0. 079 Z a 0. 03531 0.01302 819 2. 71 0. 007 0.03540 0. 01303 819 2. 72 0. 0067 Z r -0.03371 0.01637 819 -2.06 0. 040 -0.03415 0. 01639 819 -2.08 0. 0375 Z 5 0. 06201 0.01940 819 3. 20 0. 001 0.05338 0. 01827 819 2. 92 0. 0036 Z 9 0. 08917 0.01429 819 6. 24 0. 000 0.08637 0. 01414 819 6. 11 0. 00000 ZZ ee --- --- --- --- --- --- --- --- --- --- ZZ 55 0. 05562 0.01452 819 3. 83 0. 000 0.05652 0. 01451 819 3. 89 0. 00011 ZZ ea 0. 04671 0.01711 819 2. 73 0. 006 0.04544 0. 01710 819 2. 66 0. 0080 ZZ er -0.03051 0.01391 819 -2.19 0. 029 -0.02795 0. 01379 819 -2.03 0. 043 ZZ e5 0. 03208 0.01458 819 2. 20 0. 028 0.03080 0. 01456 819 2. 12 0. 035 ZZ e9 --- --- --- --- --- --- --- --- --- --- ZZ ar --- --- --- --- --- --- --- --- --- --- ZZ a5 0. 04751 0.02095 819 2. 27 0. 024 0.04528 0. 02090 819 2. 17 0. 031 ZZ a9 0. 01833 0.01397 819 1. 31 0. 190 ZZ 59 --- --- --- --- --- --- --- --- --- --- ZZ r9 --- --- --- --- --- --- --- --- --- ---

0.8516 0. 8507
0.1298 0. 1300 2
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