### 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 **L .**  **3**

**Model	Fitting	Information	for** 

# Formaldehyde **( Bag	1**  **)**

This appendix summarizes model fitting for Formaldehyde (Bag 1) . Model-fitting techniques and approaches are described in Section 8 .7. Features of the data and modeling for this compound are listed below. Fuel-parameter matrix: FULL No. measurements: 9 5 6 No. vehicles: 15 No. censored values: 0 Modeling approach: MIXED MODEL

### 2 **Models fit for Formaldehyde (Bag 1).** Model Term Notation Model Full Model FM4 FM5 FM6 FM7 Linear Effects 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 ● ● 

### × T90 × T90 ZZ 99 ● ● ● ● 

### × T50 × T90 ZZ 59 ● ● ● ● ● 

### × RVP × T90 ZZ r9 ● 

### × 

### Fitting history for Bag**- 1 Formaldehyde**  **– with “** **FM 7** **” selected as the reduced**  **model.** 

## Fit Parameters Test with respect to Full Test with respect to Previous Model 

### Model p -2ln L BIC 1 

### Dev. 1 

### d Pr>χ 2 

### Dev. d Pr>χ 2 

### Full 17 - 102.866 -48.705 FM4 13 - 101.651 - 58.322 1.215 4 0.876 FM5 12 - 100.336 - 59.715 2.530 5 0.772 1.315 1 0.252 FM6 11 -99.040 -61.127 3.826 6 0.700 1.296 1 0.255 FM7 2 

### 10 -95.848 -60.643 7.018 7 0.427 3.192 1 0.074 Linear Effects 5 - 13.166 8.498 89.700 12 0.000000 82.682 5 0.000000 1 A lower value indicates a better fit. 2 Selected as “best fit” with respect to the 17 -term full model. Note that based on the history, FM6 is actually the “best fit,” however, we have retained FM7 due to the decision to exclude the T90 × T90 term from final model fitting. See Section 7.2.1. 1 The deviation is the difference in the -2loglik statistics for the nested and reference models, respectively, per 

### Error! **Reference source not found.** 

.

### 3

**Coefficients and Type -** **III Tests of Effect for the Full**  **and Best -** **Fit Models –**  **Formaldehyde (Bag 1).** Effect Full Model Best-Fit Model ( FM7 ) Estimate Std.Err. d.f. t-value Pr>t Estimate Std.Err. d.f. t-value Pr>t 

### Intercept

- 5.9771 0.1498 15 - 39.9 0.000000 - 5.9771 0.1498 15 - 39.9 0.000000 

### Z e 0.2279 0.01234 898 18.5 0.000000 0.2299 0.009640 898 23.8 0.000000 

### Z a 0.03528 0.008841 898 3.99 0.000071 0.02822 0.007979 898 3.54 0.00043 

### Z r -0.05202 0.01234 898 -4.21 0.000028 -0.04718 0.008457 898 - 5.58 0.000000 

### Z 5 0.1577 0.01738 898 9.07 0.000000 0.1672 0.01001 898 16.7 0.000000 

### Z 9 0.1357 0.01064 898 12.7 0.000000 0.1302 0.007360 898 17.7 0.000000 

### ZZ ee -0.01498 0.01475 898 - 1.02 0.31 

### ZZ 55 0.05026 0.01251 898 4.02 0.000064 0.05262 0.008341 898 6.31 0.000000 

### ZZ ea 0.02017 0.01241 898 1.63 0.10 0.01651 0.007340 898 2.25 0.025 

### ZZ er 0.004100 0.008366 898 0.490 0.62 

### ZZ e5 -0.03686 0.01594 898 -2.31 0.021 -0.01627 0.008177 898 - 1.99 0.047 

### ZZ e9 0.02181 0.01023 898 2.13 0.033 0.02004 0.008838 898 2.27 0.024 

### ZZ ar 0.007384 0.01535 898 0.481 0.63 

### ZZ a5 -0.006739 0.01645 898 -0.41 0.68 

### ZZ a9 -0.01036 0.008437 898 - 1.23 0.22 

### ZZ 99 0.02104 0.01435 898 1.47 0.14 

### ZZ 59 0.03974 0.01080 898 3.68 0.00025 0.03489 0.009322 898 3.74 0.00019 

### ZZ r9 -0.003140 0.009498 898 -0.331 0.74 2 veh 

##  0.3360 0.3358 2  

##  0.1395 0.1406