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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.1f Final	Model	Fitting**  **Total	Hydrocarbons	(THC)	( Bag	3**  **)**

No. Observations: 956 No. Vehicles: 1 5 No. censored measurements: 2 No. missing measurements: 0 No. measurements removed: 0 Model Ty pe: Mixed model

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### I.1f **.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 models respecting hierarchy (CLOSEUP of previous figure).** 

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**THC (** **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**  **- 9**  **comprise the “superset” for final m odel**  **- fitting).** 

### 5 **Models fit for THC ( Bag 3**  **): (all models include an intercept term).** Model Term Notation Model Superset SM2 1 SM4 SM5 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 --- --- --- --- 1 Represents “Superset minus 2,” etc. 2 Not nested within SM4; test with respect to SM2. **THC ( Bag 3**  **): 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 10 527.403 559.900 SM 2 2 8 530.138 557.218 2.735 2 0.255 SM4 6 556.555 534.890 4.753 2 0.0929 SM5 5 562.345 543.388 13.250 3 0.00413
1 A lower value indicates a better fit. 2 Best fit with respect to the 1 1
-term design model. 3 Not nested within SM4; test with respect to SM2.

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**THC (** **Bag 3 ): 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.1f **.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**  **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 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 -**  **9 comprise the “superset” for final model** **- fitting).** 

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NOTE: Model fitting for 16
- term extended model has results identical to that for the 11
- term design model, as presented above.