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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 **H.5 Final	Model	Fitting**  **Carbon	Monoxide (C**  **O )	(**  **Bag	3 )** 

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

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### H.5 **.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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**CO (** **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**  **- 6**  **comprise the “superset” for final m odel**  **- fitting).** 

### 5 **Models fit for CO**  **( Bag 3**  **): (all models include an intercept term).**

Model Term Notation Model Superset SM3 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.
**CO (** **Bag 3 ): Model fitting history, starting with the**  **8 -**  **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 8 1182.918 1209.999 SM 3 2 5 1184.850 1203.806 1.931 3 0.587
1 A lower value indicates a better fit. 2 Best fit with respect to the 1 1
-term design model.

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**CO (** **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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### H.5 **.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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**CO (** **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 -**  **6 comprise the “superset” for final model** **- fitting).** 



### NOTE: The results of model fitting for the extended model are identical to those for the design model, as presented above.