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**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.1e Final	Model	Fitting**  **Total	Hydrocarbons	(THC)	(Bag 2**  **)**

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

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## I.1e **.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).** 

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**Design Model (11 -** **terms): Bayesian**  **Information Criterion (BIC) vs. number of terms in model ( p**  **) for all possible mod**  **els respecting hierarchy (CLOSEUP of previous figure).**

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**THC (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 -**  **5 comprise the “superset” for final model** **- fitting).** 

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

Model Term Notation Model Superset SM 3 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 3 ,” etc. 

### THC (Bag **2 ): 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 10 195.334 226.113 SM 3 2 7 201.213 224.297 5.879 3 0.118
1 A lower value indicates a better fit. 2 Best fit with respect to the 1 1
-term design model.

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**THC (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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## I.1e **.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 hierarc hy (CLOSEUP**  **of previous figure** **).**

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**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).** 

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**THC (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).**

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

Model Term Notation Model Superset SM 1 1 SM 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 --- 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. ” 

### THC (**Bag 2 ): 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 11 190.795 224.139 SM 1 2 10 192.466 223.245 1.671 1 0.196 SM 4 3 7 203.136 226.220 10.670 3 0.0137
1 A lower value indicates a better fit. 2 Best fit with respect to the 16
-term extended model. 3 Fit because the linear term for Aromatics appears insignificant in The superset model; therefore, dropped aromatics and its interactions. Test results indicate that these three terms contribute to fit.

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

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