### 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.4m**
**Final	Model	Fitting Methane**  **(C H**  **4** 

## )	(Bag	1)

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

### 2



## I.4m **.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 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** 
**- 7**  **comprise the “superset” for final model** 
**- fitting).** 

**Rank p**  **BI**

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

1 10 -506.33 

### • • • • • • • • • 2 7 -505.646 

### • • • • • • 3 9 -505.54 

### • • • • • • • • 4 11 -505.305 

### • • • • • • • • • • 5 9 -505.278 

### • • • • • • • • 6 8 -504.925 

### • • • • • • • 7 12 -504.911 

### • • • • • • • • • • •

8 11 -503.724 

### • • • • • • • • • • 9 10 -503.703 

### • • • • • • • • • 10 8 -503.404 

### • • • • • • • 11 8 -503.314 

### • • • • • • • 12 8 -503.053 

### • • • • • • • 13 10 -503.043 

### • • • • • • • • • 14 10 -503.037 

### • • • • • • • • • 15 10 -502.965 

### • • • • • • • • • 16 9 -502.745 

### • • • • • • • • 17 9 -502.734 

### • • • • • • • • 18 9 -502.266 

### • • • • • • • • 19 11 -501.58 

### • • • • • • • • • • 20 11 -501.43 

### • • • • • • • • • • 21 9 -500.816 

### • • • • • • • • 22 9 -500.73 

### • • • • • • • • 23 10 -500.091 

### • • • • • • • • • 24 10 -500.077 

### • • • • • • • • • 25 6 -498.114 

### • • • • • 26 8 -498.028 

### • • • • • • • 27 7 -496.925 

### • • • • • • 28 10 -496.179 

### • • • • • • • • • 29 8 -496.142 

### • • • • • • • 30 9 -496.084 

### • • • • • • • • 31 9 -495.926 

### • • • • • • • • 32 7 -495.891 

### • • • • • • 33 9 -495.731 

### • • • • • • • • 34 7 -495.578 

### • • • • • • 35 7 -495.529 

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

**s**

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

### (Bag 1): (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 1,” etc.



### CH **4** 

### (Bag 1): Model fitting history, starting with the 1 **0**
**- 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

- 542.823

- 504.911 SM1 2 

### 10

- 538.826

- 506.330 3.997 2 0.136

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

- term extended model.

### 6

**CH 4**  

### (Bag 1): 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 ter cept -3.0072 0. 1380 15 -21.8 0. 00000 -3.0074 0.1381 15 -21.8 0. 00000 Z e 0. 06938 0.00841 941 8. 25 0. 00000 0.06994 0.008428 941 8. 30 0. 00000 Z a -0.1055 0. 005865 941 -18.0 0. 00000 -0.1053 0.005876 941 -17.9 0. 00000 Z r -0.03439 0. 006698 941 -5.13 0. 00000 -0.03275 0.006627 941 -4.94 0. 00000 Z 5 0. 07516 0. 008449 941 8. 90 0. 00000 0.07554 0.008465 941 8. 92 0. 00000 Z 9 0.003600 0. 005867 941 0. 61 0.54 ZZ ee 0. 02814 0.01129 941 2. 49 0. 013 0.02844 0. 01131 941 2. 51 0. 012 ZZ 55 0. 05185 0. 008457 941 6. 13 0. 00000 0.05170 0.008474 941 6. 10 0. 00000 ZZ ea 0. 02049 0. 005737 941 3. 57 0. 00037 0.02088 0.005745 941 3. 63 0. 00029 ZZ er 0.008907 0. 005852 941 1. 52 0.13 0.01082 0.005779 941 1. 87 0. 062 ZZ e5 0. 02983 0.01212 941 2. 46 0. 014 0.03048 0. 01213 941 2. 51 0. 012 ZZ e9 0. 01138 0. 005759 941 1. 98 0. 048

0.2853 0.2855 0. 03001 0. 03014 2 ve h 

### 
2  

###  2 veh 

### 
2  

### 

### 7



## I.4m **.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 previo**  **us 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 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**  **comprise the “superset” for final model**

**- fitting).**  **Rank p**  **BI**

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

1 15 -5 34. 546 

### • • • • • • • • • • • • • • 2 16 -5 32. 551 

### • • • • • • • • • • • • • • • 3 16 -5 32. 341 

### • • • • • • • • • • • • • • • 4 13 -5 32. 065 

### • • • • • • • • • • • • 5 14 -5 31. 548 

### • • • • • • • • • • • • • 6 14 -5 31. 484 

### • • • • • • • • • • • • • 7 13 -5 31. 384 

### • • • • • • • • • • • • 8 15 -5 31. 224 

### • • • • • • • • • • • • • •

9 12 -5 30. 726 

### • • • • • • • • • • • 10 17 -5 30. 397 

### • • • • • • • • • • • • • • • • 11 11 -5 30. 391 

### • • • • • • • • • • 12 14 -529.83 

### • • • • • • • • • • • • • 13 14 -529.57 

### • • • • • • • • • • • • • 14 13 -5 29. 491 

### • • • • • • • • • • • • 15 14 -5 29. 458 

### • • • • • • • • • • • • • 16 14 -5 29. 368 

### • • • • • • • • • • • • • 17 14 -5 29. 357 

### • • • • • • • • • • • • • 18 15 -5 29. 338 

### • • • • • • • • • • • • • • 19 15 -5 29. 277 

### • • • • • • • • • • • • • • 20 13 -5 29. 262 

### • • • • • • • • • • • • 21 15 -5 29. 258 

### • • • • • • • • • • • • • • 22 16 -5 29. 107 

### • • • • • • • • • • • • • • • 23 15 -5 28. 932 

### • • • • • • • • • • • • • • 24 14 -5 28. 751 

### • • • • • • • • • • • • • 25 14 -5 28. 529 

### • • • • • • • • • • • • • 26 12 -5 28. 297 

### • • • • • • • • • • • 27 14 -5 28. 194 

### • • • • • • • • • • • • • 28 12 -5 28. 121 

### • • • • • • • • • • • 29 12 -528.07 

### • • • • • • • • • • • 30 13 -5 28. 062 

### • • • • • • • • • • • • 31 13 -5 28. 024 

### • • • • • • • • • • • • 32 12 -5 27. 945 

### • • • • • • • • • • • 33 12 -5 27. 773 

### • • • • • • • • • • • 34 12 -5 27. 751 

### • • • • • • • • • • • 35 15 -5 27. 366 

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

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

### (Bag 1): (all models include an intercept term).

Model Term Notation Model Superset SM 2 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 ● 

### ×



### CH **4** 

### (Bag 1): 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 17

- 581.85 0

- 530.397 SM2 2 

### 1 5

- 580.583

- 534.546 1.267 2 0.531

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

- term extended model.

### 11

**CH 4**  

### (Bag 1): **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 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 -3.0065 0. 1380 15 -21.8 0.000000 -3.0068 0.1380 15 -21.8 0.000000 Z e 0. 09137 0. 009954 941 9. 18 0.000000 0.08877 0.009439 941 9. 40 0.000000 Z a -0.09725 0. 006246 941 -15.6 0.000000 -0.09816 0.006199 941 -15.8 0.000000 Z r -0.02406 0. 008404 941 -2.86 0.0043 -0.02455 0.008296 941 -2.96 0.0032 Z 5 0. 10813 0.01109 941 9. 75 0.000000 0. 1059 0. 01067 941 9. 92 0.000000 Z 9 0.006944 0. 006434 941 1. 08 0.28 0. 008573 0.006196 941 1. 38 0. 17 ZZ ee 0. 03479 0.01160 941 3. 00 0.0028 0.03133 0. 01113 941 2. 81 0.0050 ZZ 55 0. 06151 0. 009467 941 6. 50 0.000000 0.05882 0.008899 941 6. 61 0.000000 ZZ ea 0. 03944 0. 009387 941 4. 20 0.000029 0.03977 0.009181 941 4. 33 0.000016 ZZ er 0.005566 0. 006365 941 0. 87 0.38 ZZ e5 0. 03118 0.01226 941 2. 54 0. 011 0.02883 0. 01205 941 2. 39 0. 017 ZZ e9 0. 02377 0. 007526 941 3. 16 0.0016 0.02655 0.006892 941 3. 85 0. 00013
ZZ ar 0. 02957 0.01017 941 2. 91 0.0037 0.02791 0.009975 941 2. 80 0.0052 ZZ a5 0. 02268 0.01133 941 2. 00 0. 046 0.02585 0. 01075 941 2. 41 0. 016 ZZ a9 0. 03032 0. 006365 941 4. 76 0.000002 0.03072 0.006248 941 4. 92 0.000001 ZZ 59 0. 02094 0. 008467 941 2. 47 0. 014 0.02280 0.007557 941 3. 02 0.0026 ZZ r9 -0.005353 0. 007195 941 -0.744 0.46

0.2853 0.2853 0. 02879 0. 02883 2 ve h 

### 
2  

###  2 veh 

### 
2  

### 