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

No. Observations: 956 No. Vehicles: 15 No. censored measurements: 0 No. missing measurements: 0 No. measurements removed: 0 Model Ty pe: Mixed model

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## I.1d **.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 hierar** **chy (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 1): 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**  **- 5**  **comprise the “superset” for final model -** **fitting).**

### 5 **Models fit for THC (Bag 1): (all models include an intercept term).** 

Model Term Notation Model Superset SM1 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 1,” etc. 

### THC (Bag 1): Model fitting history, starting with the 1 **0 -** **term superset model.**



### Fit Parameters Test with respect to Previous Model 

### Model p -2 ln

L BIC 1 

### Dev. d Pr>χ 2 Superset 12 225.176 263.089 SM1 2 11 225.426 260.631 0.250 1 0.62
1 A lower value indicates a better fit. 2 Best fit with respect to the 16
-term extended model.

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**THC (Bag 1): 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.1d **.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 1): 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 1): (all models include an intercept term).**

Model Term Notation Model Superset SM2 1 SM6 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 2 , etc. ” 

### THC (Bag 1): Model fitting history, starting with the 15 **- term superset model.**  

### Fit Parameters Test with respect to Previous Model 

### Model p -2 ln

L BIC 1 

### Dev. d Pr>χ 2 Superset 16 196.798 245.543 SM2 2 14 199.598 242.927 2.800 2 0.247 SM6 10 229.637 262.134 30.039 4 0.0000048
1 A lower value indicates a better fit. 2 Best fit with respect to the 16
-term extended model.

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**THC (Bag 1): Coefficients and Tests of Effect for the Superset and Reduced Models, with respect**  **to the 1 6**  **- term**  **extended model.**  Effect Full Model (superset) Reduced Model (SM2)

Estimate Std.Err. d.f. t-value Pr> t Estimate Std.Err. d.f. t-value Pr> t Intercept

- 0.8653 0.09410 15
- 9.20 <0.0001
- 0.8658 0.09407 15
- 9.20 <0.0001 Z e 0.07607 0.01436 941 5.30 <0.0001 0.06794 0.01342 941 5.06 <0.0001 Z a 0.08474 0.009469 941 8.95 <0.0001 0.08344 0.00943 941 8.85 <0.0001 Z r - 0.03584 0.01264 941
- 2.83 0.0047
- 0.04669 0.01016 941
- 4.60 <0.0001 Z 5 0.1602 0.01622 941 9.88 <0.0001 0.1490 0.01446 941 10.30 <0.0001 Z 9 0.01582 0.009786 941 1.62 0.11 0.01434 0.009179 941 1.56 0.12 ZZ ee 0.04604 0.01708 941 2.69 0.0072 0.04065 0.01677 941 2.22 0.016 ZZ 55 0.0818 0.01354 941 6.04 <0.0001 0.07555 0.01299 941 5.82 <0.0001 ZZ ea 0.03790 0.01415 941 2.68 0.0075 0.02297 0.008769 941 2.62 0.0090 ZZ er 0.006772 0.009678 941 0.700 0.48 ZZ e5 0.03790 0.01839 941 2.06 0.040 0.03426 0.01827 941 1.87 0.061 ZZ e9 0.04627 0.01053 941 4.39 <0.0001 0.04782 0.01048 941 4.56 <0.0001 ZZ ar 0.03977 0.01517 941 2.62 0.0089 0.02553 0.01206 941 2.12 0.035 ZZ a5 0.02101 0.01724 941 1.22 0.22 ZZ a9 0.02087 0.009634 941 2.17 0.031 0.02260 0.009506 941 2.38 0.018 ZZ 59 0.05255 0.01161 941 4.53 <0.0001 0.05004 0.01147 941 4.36 <0.0001 ZZ r9 ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- 2 veh 

###  0.1317 0.1317 2  

###  0.06667 0.06687