### 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 **H.4 Final	Model	Fitting**  **Carbon	Monoxide (C**  **O )	(Bag**  **2 )** 

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



## H.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

**CO (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). (Ter ms included in models**  **ranked 1 -**  **5 comprise the “superset” for final model** **- fitting).** 

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

Model Term Notation Model Superset SM3 1 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 3,” etc.


### CO **(Bag 2**  **): Model fitting history, starting with the 8**  **- term superset model.** 



### Fit Parameters Test with respect to Previous Model 

### Model p -2 ln

L BIC 1 

### Dev. d Pr>χ 2 Superset 9 828.049 857.838 SM 3 6 831.913 853.577 3.864 3 0.277 SM4 2 5 832.664 851.620 0.751 1 0.386
1 A lower value indicates a better fit. 2 Best fit with respect to the 1 1
-term design model.

### 5

**CO (Bag**  **2 ): Coefficients and Tests of Effect for the Superset and Reduced Models, with respect to**  **the 1 1**  **- term**  **design model.** 

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## H.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 In**  **formation Criterion (BIC) vs. number of terms in model (**  **p ) for subset of models respecting hierarchy (CLOSEUP**  **of previous figure** **).**

### 7

**CO (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 comprise the “superset” for final model** **- fitting).** 

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

Model Term Notation Model Superset SM 3 1 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 --- --- --- Arom × RVP ZZ ar --- --- --- Arom × T50 ZZ a5 --- --- --- Arom × T90 ZZ a9 --- --- --- T50 × T90 ZZ 59 ● ● ● RVP × T90 ZZ r9 ● × 1 denotes “Superset minus 3, etc. ” 

### CO **( 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 BIC 1 

### Dev. d Pr>χ 2 Superset 10 826.828 859.325 SM 3 7 828.868 853.241 2.040 3 0.564 SM4 2 6 829.667 851.331 0.798 1 0.37
1 A lower value indicates a better fit. 2 Best fit with respect to the 16
-term extended model.

### 9

**CO (** **Bag 2 ): Coefficients and Tests of Effect for the Superset and Reduced Models, with respect to**  **the 1 6** **- term**  **extended model.**