### 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.4o**

**Final	Model	Fitting**

**Methane (C**  **H 4**  

## )	( **Bag	3 )** 

No. Observations: 893

No. Vehicles: 1 4 (drop Corolla)

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

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

### 2



## I.4o **.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 3 ): 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 7 -353.062 

### • • • • • • 2 8 -352.229 

### • • • • • • • 3 8 -351.155 

### • • • • • • • 4 8 -351.109 

### • • • • • • • 5 9 -350.906 

### • • • • • • • • 6 8 -350.865 

### • • • • • • • 7 8 -350.778 

### • • • • • • •

8 9 -350.017 

### • • • • • • • • 9 6 -349.815 

### • • • • • 10 9 -349.594 

### • • • • • • • • 11 9 -349.567 

### • • • • • • • • 12 7 -349.505 

### • • • • • • 13 7 -349.226 

### • • • • • • 14 9 -349.218 

### • • • • • • • • 15 9 -349.116 

### • • • • • • • • 16 9 -349.068 

### • • • • • • • • 17 10 -349.003 

### • • • • • • • • • 18 9 -348.894 

### • • • • • • • • 19 10 -348.842 

### • • • • • • • • • 20 6 -348.693 

### • • • • • 21 9 -348.572 

### • • • • • • • • 22 7 -348.469 

### • • • • • • 23 10 -348.27 

### • • • • • • • • • 24 8 -348.16 

### • • • • • • • 25 7 -348.083 

### • • • • • • 26 8 -348.027 

### • • • • • • • 27 7 -347.969 

### • • • • • • 28 10 -347.863 

### • • • • • • • • • 29 7 -347.691 

### • • • • • • 30 10 -347.481 

### • • • • • • • • • 31 10 -347.384 

### • • • • • • • • • 32 8 -347.236 

### • • • • • • • 33 10 -347.21 

### • • • • • • • • • 34 11 -347.144 

### • • • • • • • • • • 35 10 -347.142 

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

**s**

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

### ( **Bag 3 ): (all models include an intercept term).** 

Model Term Notation Model Superset SM2 1 SM3 SM4 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 3 ): 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

- 380.510

- 346.200 SM 2 2 9

- 379.936

- 350.907 0.576 2 0.750 SM3 8

- 378.619

- 352.229 1.317 1 0.251 SM4 2 7

- 376.814

- 353.062 1.805 1 0.179

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

- term design model.

### 6

**CH 4**  

### ( **Bag 3 ): 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 M4)
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 -4.4735 0. 1789 14 -25.0 0.000000 -4.4742 0.1789 14 -25.0 0.000000
Z e 0. 02354 0. 009267 871 2. 54 0. 011 0.02805 0.007619 871 3. 68 0. 00025
Z a -0.09565 0. 006507 871 -14.7 0.000000 -0.09578 0.006502 871 -14.7 0. 00000
Z r -0.008909 0. 007373 871 -1.21 0.23
Z 5 0. 02400 0. 009333 871 2. 57 0. 010 0.03025 0.007967 871 3. 80 0. 00016
Z 9 0. 01811 0. 006477 871 2. 80 0.0053 0.01691 0.006375 871 2. 65 0.0081
ZZ ee -0.000506 0.01230 871 -0.0411 0.97
ZZ 55 0. 01093 0. 009364 871 1. 17 0.24
ZZ ea 0. 01463 0. 006349 871 2. 30 0. 021 0.01528 0.006289 871 2. 43 0. 015
ZZ er --- --- --- --- --- --- --- --- --- --- ZZ e5 -0.01724 0.01321 871 -1.30 0.19 -0.02079 0.006491 871 -3.20 0.0014
ZZ e9 0.004783 0. 006314 871 0.758 0.45

0.4478 0.4477

0. 03425 0. 03439 2

ve h 

### 

2

 

###  2 veh 

### 

2

 

### 

### 7



## I.4o **.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 Criteri on (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 3 ): 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).** 



### NOTE: Model fitting with respect to the 16

- term extended model gives identical results to those obtained for the 11

- term design model, as presented above. **Rank p**  **BI**

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

1 7 -3 53. 062 • • • • • • 2 8 -3 52. 229 • • • • • • • 3 8 -3 51. 155 • • • • • • • 4 8 -3 51. 109 • • • • • • • 5 9 -3 50. 906 • • • • • • • •

6 8 -3 50. 865 • • • • • • • 7 8 -3 50. 778 • • • • • • • 8 10 -3 50. 633 • • • • • • • • • 9 8 -3 50. 531 • • • • • • • 10 8 -3 50. 516 • • • • • • • 11 8 -3 50. 429 • • • • • • • 12 9 -3 50. 017 • • • • • • • • 13 6 -3 49. 815 • • • • • 14 9 -3 49. 727 • • • • • • • • 15 9 -3 49. 715 • • • • • • • • 16 9 -349.66 • • • • • • • • 17 9 -3 49. 639 • • • • • • • • 18 9 -3 49. 594 • • • • • • • • 19 9 -3 49. 567 • • • • • • • • 20 7 -3 49. 505 • • • • • • 21 7 -3 49. 226 • • • • • • 22 9 -3 49. 218 • • • • • • • • 23 7 -3 49. 155 • • • • • • 24 9 -3 49. 116 • • • • • • • • 25 9 -3 49. 068 • • • • • • • • 26 10 -3 49. 003 • • • • • • • • • 27 9 -3 48. 894 • • • • • • • • 28 10 -3 48. 842 • • • • • • • • • 29 8 -3 48. 707 • • • • • • • 30 6 -3 48. 693 • • • • • 31 9 -3 48. 636 • • • • • • • • 32 11 -3 48. 629 • • • • • • • • • • 33 9 -348.62 • • • • • • • • 34 9 -3 48. 594 • • • • • • • • 35 9 -3 48. 574 • • • • • • • • **De si**  **gn T**  **erm s**  **Ex te**  **nd ed**  **Te rm**  **s**