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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 **J.6 Final	Model	Fitting**  **Particulate	Matter (**  **PM )	(**  **Bag	3 )** 

No. Observations: 871 No. Vehicles: 15 No. censored measurements: 82 No. missing measurements: 2 No. measurements removed: 1 Model Ty pe: Tobit regression

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**J.6 .1		Model	Fitting	based	on	the	11**  **- term	design	model.** 

**Models fit for PM ( Bag 3** **): (Grand Intercept not fit by Tobit models).** Model Term Notation Model Full FM1 1 

### FM2 FM3 FM4 FM5 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 Indicates “Full minus 1,” etc. 

### PM (**Bag 3 ): Model fitting history, starting with the 11**  **- term design model.** 



### Fit Parameters Test with respect to Previous Model 

### Model p- 1 1



### -2 ln L Dev. d Pr>χ 2 

### Full Model 11 3224.082 FM1 10 3224.175 0.093 1 0.760 FM2 9 3224.623 0.448 1 0.503 FM3 8 3224.86 0.237 1 0.626 FM4 7 3225.436 0.576 1 0.448 FM5 6 3226.131 0.695 1 0.404
1 Total number of terms excludes the intercept, as the Tobit models do not fit intercepts. 2 Best fit with respect to the 17

-term extended model.

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**PM (** **Bag 3 ):**  **Co efficients and Tests of Effect for the**  **Full and Reduced Models, with respect to the**  **1 1**  **- term**  **design model.**  

### Ef fe ct Fu ll Model Reduced Model (F M5) Es ti mate Std.E

rr. d. f. χ2 - v al

ue Pr>χ2 Es ti

mate Std.E

rr. d. f. χ

2 - v al ue Pr>χ

2 Intercept 1 -0.3539 Z e -0.0003 0.0656 1 0.000000 1.00 0.0173 0.0579 1 0. 090 0. 77 Z a 0. 0170 0.0457 1 0. 140 0.71 0.0216 0.0455 1 0. 220 0. 64 Z r -0.1082 0.0522 1 4.30 0. 038 -0.1098 0.0499 1 4. 840 0. 03 Z 5 0. 0079 0.0658 1 0. 010 0.90 0.0167 0.0616 1 0. 070 0. 79 Z 9 -0.0337 0.0457 1 0.54 0.46 ZZ ee -0.0593 0.0879 1 0.46 0.50 ZZ 55 -0.0527 0.0658 1 0.64 0.42 ZZ ea 0. 0975 0.0447 1 4.76 0. 029 0.1023 0.0441 1 5. 390 0. 02 ZZ er -0.0402 0.0456 1 0.78 0.38 ZZ e5 -0.1885 0.0943 1 4.00 0. 046 -0.1218 0.0455 1 7. 170 0. 01 ZZ e9 0. 0136 0.0448 1 0. 090 0.76
0.1178 1.3431 1 Notfi t by T obitmodel; calculat ed manually from indi vidual vehicle int ercep ts
. 1 2 veh 

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2  

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**J.6 .2	Model	Fitting	based	on	the	1**  **7 -**  **term	extended	model.**

**Models fit for PM**  **( Bag 3** **): (Grand Intercept not fit by Tobit models).**  Model Term Notation Model Full FM4 1 

### FM5 FM6 FM7 FM8 FM9 FM10 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 ● ● ● 

### × T90 × T90 ZZ 99 ● 

### × Arom × RVP ZZ ar ● ● ● ● ● ● ● ● 

### Arom × T50 ZZ a5 ● 

### × Arom × T90 ZZ a9 ● ● ● ● ● ● 

### × T50 × T90 ZZ 59 ● 

### × RVP × T90 ZZ r9 ● 

### × 1 Indicates “Full minus 4,” etc.



### PM **( Bag 3** **): Model fitting history, starting with the 1**  **7 -** **t erm**  **extended model.** 



### Fit Parameters Test with respect to Previous Model 

### Model p- 1 1



### -2 ln L Dev. d Pr>χ 2 

### Full Model 17 3215.611 FM4 13 3215.883 0.272 4 0.992 FM5 12 3216.627 0.744 1 0.388 FM6 11 3217.959 1.332 1 0.248 FM7 10 3219.173 1.214 1 0.271 FM8 9 3220.762 1.589 1 0.207 FM9 8 3222.431 1.669 1 0.196 FM10 7 3222.609 0.178 1 0.673

1 Total number of terms excludes the intercept, as the Tobit Models do not fit intercepts

. 2 Best fit with respect to the 1 7

-term extended model.

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**PM (** **Bag 3 ):**  **Co efficients and Tests of Effect for the**  **Full and Reduced Models, with respect to the**  **17 -** **term extended**  **model .**  

### Ef fe ct Fu ll Model Reduced Model (FM10) Es ti mate Std.E

rr. d. f. χ2 - v al

ue Pr>χ2 Es ti

mate Std.E

rr. d. f. χ

2 - v al ue Pr>χ

2 Intercept 1 Z e -0.0434 0.0810 1 0.29 0.59 -0.0212 0.0613 1 0.12 0. 73 Z a -0.0024 0.0552 1 0.0000 0.97 0.0186 0.0455 1 0.17 0. 68 Z r -0.1395 0.0754 1 3.42 0.06 -0.1275 0.0507 1 6.33 0.012 Z 5 -0.0311 0.1081 1 0. 080 0.77 -0.0411 0.0687 1 0.36 0. 55 Z 9 0. 0031 0.0593 1 0.000000 0.96 ZZ ee -0.0751 0.0919 1 0.67 0.41 ZZ 55 -0.1023 0.0750 1 1.86 0.17 ZZ ea 0. 0544 0.0748 1 0.53 0.47 0.0849 0.0450 1 3.57 0.059 ZZ er -0.0742 0.0506 1 2.15 0.14 ZZ e5 -0.1512 0.0970 1 2.43 0.12 -0.0824 0.0500 1 2.71 0. 10 ZZ e9 0. 0399 0.0617 1 0.42 0.52 ZZ ar -0.1631 0.0944 1 2.99 0.08 -0.1062 0.0566 1 3.53 0.060 ZZ a5 -0.0107 0.1016 1 0. 010 0.92 ZZ a9 0. 0892 0.0515 1 3.01 0.08 ZZ 59 -0.0241 0.0670 1 0.13 0.72 ZZ r9 0.00020 0.0582 1 0.000000 1.00

1. 3351 1.3405 1 Notfitby T obi

t mo del. 1 2 veh 

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