### 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 **G.4**

**Final	Model	Fitting**
**Oxides	of	Nitrogen (**  **N O**  **x** 

## )	( **Bag	2 )** 

No. Observations: 8 93

No. Vehicles: 1 4 (drop Cobalt )

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

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

### 2



## G.4 **.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

**NO x**  

### ( **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 inclu ded in models**  **ranked 1**

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

**- fitting).** 

**Rank p**  **BI**

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

1 3 1105.17 

### • • 2 4 1106.57 

### • • • 3 4 1107.66 

### • • • 4 4 1107.67 

### • • • 5 4 1107.68 

### • • • 6 4 1107.74 

### • • • 7 5 1108.17 

### • • • • 8 5 1109.03 

### • • • • 9 5 1109.06 

### • • • • 10 5 1109.11 

### • • • •

11 5 1109.20 

### • • • • 12 5 1110.20 

### • • • • 13 5 1110.20 

### • • • • 14 5 1110.21 

### • • • • 15 5 1110.21 

### • • • • 16 5 1110.23 

### • • • • 17 5 1110.25 

### • • • • 18 5 1110.26 

### • • • • 19 5 1110.29 

### • • • • 20 5 1110.33 

### • • • • 21 6 1110.68 

### • • • • • 22 6 1110.69 

### • • • • • 23 6 1110.71 

### • • • • • 24 6 1110.81 

### • • • • • 25 2 1111.53 

### • 26 6 1111.53 

### • • • • • 27 6 1111.58 

### • • • • • 28 6 1111.58 

### • • • • • 29 6 1111.62 

### • • • • • 30 6 1111.66 

### • • • • • 31 6 1111.67 

### • • • • • 32 6 1111.71 

### • • • • • 33 6 1111.73 

### • • • • • 34 6 1111.80 

### • • • • • 35 6 1112.75 

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

### 4 **Models fit for NO**  **x** 

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

Model Term Notation Model Superset SM 4 1 

### SM 6 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 4, ” etc.



### NO **x** 

### ( **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 9 1089.365 1118.395 SM 4 5 1089.700 1108.173 0.335 4 0.987 SM 6 2 

### 3 1091.971 1105.166 2.271 0.321

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

- term design model.

### 5

**NO x**  

### ( **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 M6)
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 -4.5680 0. 1844 14 -24.8 0. 00000 -4.5692 0.1842 14 -24.8 0.000000
Z e 0. 05813 0.01952 879 2. 98 0.0030 0.06299 0. 01444 879 4. 36 0.000014
Z a 0. 04469 0.01492 879 3. 00 0.0028 0.04407 0. 01465 879 3. 01 0.0027
Z r -0.01729 0.01653 879 -1.05 0.30
Z 5 -0.00245 0.02024 879 -0.12 0.90
Z 9 0. 00491 0.01481 879 0. 33 0.74
ZZ ee -0.00447 0.01525 879 -0.29 0.77
ZZ 55 --- --- --- --- --- --- --- --- --- --- ZZ ea 0. 00478 0.01455 879 0. 33 0.74
ZZ er 0. 01418 0.01455 879 0. 97 0.33
ZZ e5 --- --- --- --- --- --- --- --- --- --- ZZ e9 --- --- --- --- --- --- --- --- --- ---

0.4730 0.4720

0.1830 0.1836 2

ve h 

### 

2

 

###  2 veh 

### 

2

 

### 

### 6



## G.4 **.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 Criterio n (BIC) vs. number of terms in model**  **( p**  **) for subset of models respecting hierarchy (CLOSEUP of**  **previous figure ).** 

### 7

**NO x**  

### ( **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**

**- 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 3 1105.17 

### • • 2 4 1106.57 

### • • • 3 4 1107.66 

### • • • 4 4 1107.67 

### • • • 5 4 1107.68 

### • • • 6 4 1107.74 

### • • •

7 5 1108.17 

### • • • • 8 5 1109.03 

### • • • • 9 5 1109.06 

### • • • • 10 5 1109.09 

### • • • • 11 5 1109.11 

### • • • • 12 5 1109.2 

### • • • • 13 5 1109.34 

### • • • • 14 5 1109.75 

### • • • • 15 5 1110.2 

### • • • • 16 5 1110.2 

### • • • • 17 5 1110.21 

### • • • • 18 5 1110.21 

### • • • • 19 5 1110.23 

### • • • • 20 5 1110.25 

### • • • • 21 5 1110.26 

### • • • • 22 5 1110.29 

### • • • • 23 5 1110.33 

### • • • • 24 6 1110.61 

### • • • • • 25 6 1110.66 

### • • • • • 26 6 1110.68 

### • • • • • 27 6 1110.69 

### • • • • • 28 6 1110.71 

### • • • • • 29 6 1110.75 

### • • • • • 30 6 1110.81 

### • • • • • 31 6 1111.3 

### • • • • • 32 6 1111.42 

### • • • • • 33 2 1111.53 

### • 34 6 1111.53 

### • • • • • 35 6 1111.58 

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

### 8

NOTE: the model

- fitting process for the extended model gives identical results to those from the design model, as presented above.