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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.4 Final	Model	Fitting**  **Particulate	Matter (**  **PM )	(**  **Bag	1 )** 

No. Observations: 910 No. Vehicles: 15 No. censored measurements: 45 No. missing measurements: 0 No. measurements removed: 1 Model Ty pe: Tobit regression

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**J.4 .1		Model	Fitting	based	on	the	11**  **- term	design	model.** 

**Models fit for PM (Bag 1): (Grand Intercept not fit by Tobit models).** Model Term Notation Model Full FM2 1 

### FM3 FM4 FM5 FM6 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 ● ● ● ● 

### ×



### PM (Bag 1): 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 2789.671 FM2 9 2790.118 0.447 2 0.800 FM3 8 2791.074 0.956 1 0.328 FM4 7 2793.414 2.34 1 0.126 FM5 6 2796.069 2.655 1 0.103 FM6 2 

### 5 2796.308 0.239 1 0.625
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 1 ):**  **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 M6) 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 0.6559 Z e 0. 1365 0. 05030 1 7.35 0.0067 0.1582 0. 04130 1 14.7 0.00010 Z a 0. 3840 0. 03510 1 119.96 <.0001 0.3833 0. 03480 1 121 <.0001 Z r -0.0227 0. 04000 1 0.32 0.57 Z 5 0. 0338 0. 05050 1 0.45 0.50 0.0550 0. 04310 1 1.63 0. 20 Z 9 0. 2965 0. 03510 1 71.48 <.0001 0.2923 0. 03440 1 72.2 <.0001 ZZ ee -0.0401 0. 06750 1 0.35 0.55 ZZ 55 0. 0700 0. 05050 1 1.92 0. 166 0.0935 0. 03420 1 7.46 0. 0063 ZZ ea 0. 0508 0. 03430 1 2.19 0. 139 ZZ er 0. 0295 0. 03500 1 0.71 0.40 ZZ e5 -0.0482 0. 07230 1 0.44 0.51 ZZ e9 0. 0503 0. 03440 1 2.14 0.14
0.4251

1. 0321 1.0359 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.4 .2	Model	Fitting	based	on	the**  **17 -**  **term extended	model.** 

**Models fit for PM**  **( Bag 1**  **): (Grand Intercept not fit by Tobit models).**  Model Term Notation Model Full FM3 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 3,” etc.



### PM **( Bag 1**  **): Model fitting history, starting with the 17** **- term**  **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 2804.455 FM3 14 2804.778 0.323 3 0.956 FM5 12 2805.586 0.808 2 0.668 FM6 1 1 2806.743 1.157 1 0.282 FM7 10 2809.264 2.521 1 0.112 FM8 9 2811.736 2.472 1 0.116 FM9 8 2813.991 2.255 1 0.133 FM10 2 

### 7 2814.388 0.397 1 0.529 7 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 1 ):**  **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. 1512 0.0628 1 5.80 0. 016 0.1807 0.0425 1 18.0 <.0001 Z a 0.4355 0.0428 1 104 <.0001 0.3792 0.0351 1 116.6 <.0001 Z r -0.0619 0.0585 1 1.12 0.2897 Z 5 0. 0047 0.0837 1 0. 00000 0.96 0.1004 0.0470 1 4. 6 0. 0326 Z 9 0. 3494 0.0459 1 58.0 <.0001 0.3034 0.0353 1 74.0 <.0001 ZZ ee -0.0213 0.0712 1 0. 090 0.7653 ZZ 55 0. 0790 0.0582 1 1.84 0.17 0.0806 0.0346 1 5.4 0. 0198 ZZ ea 0. 0682 0.0579 1 1.39 0.24 ZZ er 0. 0119 0.0392 1 0. 090 0.76 ZZ e5 -0.0452 0.0752 1 0.36 0.55 ZZ e9 0. 1018 0.0478 1 4.53 0. 033 0.0647 0.0349 1 3.4 0. 0636 ZZ ar -0.0602 0.0731 1 0.68 0.41 ZZ a5 -0.0340 0.0788 1 0.19 0.67 ZZ a9 0. 0551 0.0399 1 1.91 0.17 0.0665 0.0380 1 3. 1 0. 0804 ZZ 59 0. 0389 0.0520 1 0. 560 0.45 ZZ r9 -0.0558 0.0452 1 1.53 0.22

1.0443 1 Notfitby T obi

t mo del. 1 2 veh 

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