### 1

**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.3e**
**Final	Model	Fitting**
**Non**

**- Methane	Hydrocarbons**  **( NMHC**  **)	( Bag	2**  **)**

No. Observations: 8 32
No. Vehicles: 1 3 (drop Od ys sey and Siena )
No. censored measurements: 0 No. missing measurements: 0
No. measurements removed: 0 Model Ty pe: Mixed model

### 2



## I.3e **.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).**

### 3

**Design Model (11**

**- terms):**  **Bayesian Information Criterion (BIC) vs. number of terms in model (**  **p )**  **for all possible mo dels respecting hierarchy (CLOSEUP of previous figure).** 

### 4

**NMHC (**  **Bag 2 ): 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 i ncluded in**  **models ranked 1**

**- 6**  **co mprise the “superset” for final model** 

**- fitting).** 

**Rank p**  **BI**

**C**etOHAromRVPT50T90etOH×etOHT50×T50etOH×ArometOH×RVPetOH×T50etOH×T90

1 6 987.73 

### • • • • • 2 7 990.10 

### • • • • • • 3 8 990.28 

### • • • • • • • 4 8 990.75 

### • • • • • • • 5 8 990.83 

### • • • • • • • 6 9 990.94 

### • • • • • • • •

7 9 991.28 

### • • • • • • • • 8 9 991.56 

### • • • • • • • • 9 8 991.76 

### • • • • • • • 10 8 991.77 

### • • • • • • • 11 9 991.91 

### • • • • • • • • 12 10 992.01 

### • • • • • • • • • 13 9 992.15 

### • • • • • • • • 14 9 992.30 

### • • • • • • • • 15 9 992.33 

### • • • • • • • • 16 5 992.43 

### • • • • 17 10 992.49 

### • • • • • • • • • 18 9 992.83 

### • • • • • • • • 19 10 992.98 

### • • • • • • • • • 20 10 993.13 

### • • • • • • • • • 21 9 993.15 

### • • • • • • • • 22 10 993.23 

### • • • • • • • • • 23 9 993.38 

### • • • • • • • • 24 10 993.49 

### • • • • • • • • • 25 10 993.73 

### • • • • • • • • • 26 11 993.89 

### • • • • • • • • • • 27 10 994.09 

### • • • • • • • • • 28 10 994.27 

### • • • • • • • • • 29 11 994.41 

### • • • • • • • • • • 30 11 994.69 

### • • • • • • • • • • 31 7 994.71 

### • • • • • • 32 10 994.75 

### • • • • • • • • • 33 11 994.90 

### • • • • • • • • • • 34 6 994.96 

### • • • • • 35 5 995.41 

### • • • • **De si**  **gn T**  **erm**

**s**

### 5 **Models fit for NMHC**  **( Bag 2**  **): (all models include an intercept term).**

Model Term Notation Model Superset SM3 1 

### SM4 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 denotes “Superset minus 3, ” etc.



### NMHC **( Bag 2**  **): Model fitting history, starting with the 10** 

**- 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 10 961.229 992.008 SM 3 7 967.013 990.098 5.785 3 0.123 SM4 2 

### 6 967.211 987.730 0.197 1 0.657

1 A lower value indicates a better fit. 2 Best fit with respect to the 11

- term design model.

### 6

**NMHC (**  **Bag 2 ):**  **Co efficients and Tests of Effect for the Superset and Reduced Models, with**  **respect to the 1 1** 

**- term**  **design model.** 



### Effe ct Fu ll Model (su perset ) Re duced Model (S M4) Es ti ma te St d. E

rr. d. f. t -v al

ue Pr> t Es ti

ma te St d. E

rr. d. f. t -v al

ue Pr> t In ter cept -5.3253 0. 2738 13 -19.45 0. 00000 -5.3253 0.2734 13 -19.48 0. 00000 Z e 0.009380 0.01907 819 0.492 0.62 Z a 0. 03825 0.01488 819 2. 57 0. 010 0.03987 0. 01476 819 2. 70 0.0071 Z r -0.05762 0.01685 819 -3.42 0. 00066 -0.05881 0. 01555 819 -3.78 0. 00017 Z 5 0. 04836 0.02061 819 2. 35 0. 019 0.04548 0. 01567 819 2. 90 0.0038 Z 9 0. 08329 0.01480 819 5. 63 0. 00000 0.08202 0. 01478 819 5. 55 0. 00000 ZZ ee --- --- --- --- --- --- --- --- --- --- ZZ 55 0. 05627 0.01653 819 3. 41 0. 00069 0.04774 0. 01487 819 3. 21 0. 00137 ZZ ea 0. 02106 0.01447 819 1. 46 0.15 ZZ er -0.01776 0.01453 819 -1.22 0.22 ZZ e5 0. 02222 0.01638 819 1. 36 0.18 ZZ e9 --- --- --- --- --- --- --- --- --- ---

0.9722 0.9691
0.1695 0.1708 2
ve h 

### 

2
 

###  2 veh 

### 

2
 

### 

### 7



## I.3e **.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 Cr iterion (BIC) vs. number of terms in model**  **( p**  **) for subset of models respecting hierarchy (CLOSEUP of**  **previous figure ).** 

### 8

**Extended Model (16**

**- terms): Bayesian Information Criterion (BIC) vs. number of terms in model**  **( p**  **) for subset of models respecting hiera rchy (CLOSEUP of previous figure).** 

### 9

**NMHC (**  **Bag 2 ): 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**

**- 7**  **co mprise the “superset” for final model** 

**- fitting).** 

**Rank p**  **BI**

**C**etOHAromRVPT50T90etOH×etOHT50×T50etOH×ArometOH×RVPetOH×T50etOH×T90Arom×RVPArom×T50Arom×T90T50×T90RVP×T90

1 6 987.73 

### • • • • • 2 7 989.24 

### • • • • • • 3 7 989.3 

### • • • • • • 4 11 989.38 

### • • • • • • • • • • 5 7 989.61 

### • • • • • • 6 10 989.8 

### • • • • • • • • • 7 7 989.89 

### • • • • • •

8 12 990.06 

### • • • • • • • • • • • 9 7 990.1 

### • • • • • • 10 8 990.28 

### • • • • • • • 11 7 990.29 

### • • • • • • 12 8 990.75 

### • • • • • • • 13 11 990.8 

### • • • • • • • • • • 14 8 990.83 

### • • • • • • • 15 10 990.85 

### • • • • • • • • • 16 11 990.86 

### • • • • • • • • • • 17 9 990.94 

### • • • • • • • • 18 9 990.96 

### • • • • • • • • 19 8 990.99 

### • • • • • • • 20 9 991.19 

### • • • • • • • • 21 8 991.19 

### • • • • • • • 22 12 991.21 

### • • • • • • • • • • • 23 8 991.28 

### • • • • • • • 24 9 991.28 

### • • • • • • • • 25 11 991.44 

### • • • • • • • • • • 26 11 991.47 

### • • • • • • • • • • 27 8 991.49 

### • • • • • • • 28 13 991.52 

### • • • • • • • • • • • • 29 12 991.56 

### • • • • • • • • • • • 30 9 991.56 

### • • • • • • • • 31 8 991.59 

### • • • • • • • 32 8 991.63 

### • • • • • • • 33 8 991.63 

### • • • • • • • 34 8 991.63 

### • • • • • • • 35 9 991.66 

### • • • • • • • • **De si**  **gn T**  **erm s**  **Ex te**  **nd ed**  **Te rm**  **s**

### 10 **Models fit for NMHC**  **( Bag 2**  **): (all models include an intercept term).**

Model Term Notation Model Superset SM4 1 

### SM8 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 4,” etc.



### NMHC **( Bag 2**  **): Model fitting history, starting with the 9** 

**- 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 15 952.581 996.185 SM 4 2 

### 11 956.038 989.382 3.457 4 0.484 SM8 7 967.210 990.295 11.172 4 0.025

1 A lower value indicates a better fit. 2 Best fit with respect to the 16

- term extended model.

### 11

**NMHC (**  **Bag 2 ):**  **Co efficients and Tests of Effect for the Superset and**  **Reduced Models, with respect to the 1**  **6**

**- term**  **extended model.** 



### Effe ct Fu ll Model (su perset ) Re duced Model (S M4) Es ti ma te St d. E

rr. d. f. t -v al

ue Pr> t Es ti

ma te St d. E

rr. d. f. t -v al

ue Pr> t In ter cept -5.3250 0. 2740 13 -19.4 0. 00000 -5.3256 0.2739 13 -19.4 0. 00000 Z e 0. 02885 0.02218 819 1. 30 0.19 0.01334 0. 01909 819 0. 70 0. 48 Z a 0. 04286 0.01594 819 2. 69 0.0073 0.03743 0. 01483 819 2. 52 0. 012 Z r -0.03307 0.02098 819 -1.58 0.12 -0.03909 0. 01865 819 -2.10 0. 036 Z 5 0. 07846 0.02673 819 2. 93 0.0034 0.05566 0. 02080 819 2. 68 0.0076 Z 9 0. 09945 0.01660 819 5. 99 0. 00000 0.09799 0. 01610 819 6. 09 0. 00000 ZZ ee --- --- --- --- --- --- --- --- --- --- ZZ 55 0. 06524 0.01810 819 3. 60 0.00 0.05909 0. 01652 819 3. 58 0. 00037 ZZ ea 0. 06090 0.02371 819 2. 57 0. 010 0.05087 0. 01946 819 2. 61 0.0091 ZZ er -0.03344 0.01630 819 -2.05 0. 041 -0.03153 0. 01569 819 -2.01 0. 045 ZZ e5 0. 02558 0.01745 819 1. 47 0.14 0.02865 0. 01657 819 1. 73 0. 084 ZZ e9 --- --- --- --- --- --- --- --- --- ---
ZZ ar 0. 01733 0.02569 819 0. 67 0.50 ZZ a5 0. 06319 0.02923 819 2. 16 0. 031 0.05429 0. 02379 819 2. 28 0. 023 ZZ a9 0. 02290 0.01620 819 1. 41 0.16 ZZ 59 0. 00490 0.01743 819 0. 28 0.78 ZZ r9 -0.01760 0.01679 819 -1.05 0.29

0.9734 0.9723
0.1677 0.1684 2
ve h 

### 

2
 

###  2 veh 

### 

2
 

### 