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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.5 Final	Model	Fitting**  **Particulate	Matter (**  **PM )	(**  **Bag	2 )** 

No. Observations: 9 06 No. Vehicles: 15 No. censored measurements: 4 7 No. missing measurements: 2 No. measurements removed: 1 Model Ty pe: Tobit regression

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**J.5 .1		Model	Fitting	based	on	the	11**  **- term	design	model.** 

**Models fit for PM ( Bag 2** **): (Grand Intercept not fit by Tobit models).** Model Term Notation Model Full FM3 1 

### FM4 FM5 FM6 FM7 FM8 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 2 ): 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 2954.321 FM 3 8 2954.834 0.513 3 0.916 FM4 7 2955.471 0.637 1 0.425 FM 5 6 2957.466 1.995 1 0.158 FM 6 5 2959.590 2.124 1 0.145 FM7 4 2959.643 0.053 1 0.818 FM8 3 2961.414 1.771 1 0.183
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 2 ):**  **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 M8) 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 -1.3107 Z e 0. 0390 0.0552 1 0. 500 0.48 0.1126 0.0370 1 9.27 0. 0023 Z a 0. 1619 0.0384 1 17.8 <.0001 0.1662 0.0376 1 19.6 <.0001 Z r -0.0615 0.0438 1 1.97 0.16 Z 5 -0.0725 0.0553 1 1.72 0.19 Z 9 0. 1064 0.0384 1 7.69 0.0055 0.1072 0.0376 1 8.14 0. 0043 ZZ ee -0.1380 0.0739 1 3.48 0. 062 ZZ 55 -0.0143 0.0553 1 0.0700 0.80 ZZ ea 0. 0210 0.0375 1 0.31 0.58 ZZ er -0.0272 0.0383 1 0.50 0.48 ZZ e5 -0.1109 0.0795 1 1.95 0.16 ZZ e9 -0.0135 0.0377 1 0.13 0.72
0.7827

1. 1294 1.1337 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.5 .2	Model	Fitting	based	on	the**  **17 -**  **term extended	model.** 

**Models fit for PM**  **( Bag 2** **): (Grand Intercept not fit by Tobit models).**  Model Term Notation Model Full FM4 1 

### FM5 FM6 FM7 FM8 FM9 FM10 FM11 FM12 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 2** **): 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 2937.842 FM4 13 2938.618 0.776 4 0.9416 FM5 12 2939.112 0.494 1 0.4821 FM6 11 2941.062 1.95 0 1 0.1626 FM7 10 2943.444 2.382 1 0.1227 FM8 9 2945.255 1.811 1 0.1784 FM9 8 2947.232 1.977 1 0.1597 FM10 7 2949.896 2.664 1 0.1026 FM11 6 2952.334 2.438 1 0.1184 FM12 2 

### 5 2954.483 2.149 1 0.1427 7 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 2 ):**  **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 (FM12) 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. 0019 0.0679 1 0.0000 0.98 0.1158 0.0450 1.0000 6.6300 0. 0100 Z a 0. 2522 0.0461 1 30.0 <0.0001 0.1988 0.0398 1.0000 24.9000 <0.0001 Z r -0.1588 0.0630 1 6.35 0. 012 Z 5 -0.1865 0.0903 1 4.26 0. 039 -0.0037 0.0463 1.0000 0.0100 0. 9355 Z 9 0. 1566 0.0494 1 10.1 0.0015 0.0953 0.0377 1.0000 6.3900 0. 0115 ZZ ee -0.1590 0.0770 1 4.27 0. 039 ZZ 55 -0.0315 0.0629 1 0.25 0.62 ZZ ea -0.0078 0.0625 1 0. 020 0.90 ZZ er -0.0249 0.0423 1 0.35 0.56 ZZ e5 -0.1421 0.0814 1 3.05 0. 081 ZZ e9 0. 1097 0.0515 1 4.53 0. 033 ZZ ar -0.1059 0.0788 1 1.81 0.18 ZZ a5 -0.1157 0.0849 1 1.86 0.17 ZZ a9 0. 0346 0.0430 1 0.65 0.42 ZZ 59 0. 1600 0.0560 1 8.16 0.0043 0.1059 0.0402 1.0000 6.9500 0. 0084 ZZ r9 -0.0118 0.0487 1 0. 060 0.81

1. 1194 1.1295 1 Notfitby T obi

t mo del. 1 2 veh 

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