Document ID: EPA-HQ-OAR-2011-0135-0585
Agency: epa
Document Type: Supporting & Related Material
Title: 
Posted Date: 2013-04-16T04:00Z

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.4
                                       
                                       
                         Model Fitting Information for
                             Formaldehyde (Bag 2)

This appendix summarizes model fitting for Bag-2 Formaldehyde.  Model-fitting techniques and approaches are summarized in Section 8.7.  Features of the data and modeling for this compound are listed below.
Media contamination:	YES
No. measurements:	63
No. censored values:	1
Modeling approach:	MIXED MODEL
Estimated Dependent Variable model:	YES

                       Models fit for Bag-2 Formaldehyde
Model term
                                   Notation
                                     Model

                                       
                                     Full
FM1[1]
FM2
FM3
Null model[2]
                                     etOH
Ze
                                      ●
                                      ●
                                      ●
                                      ●
                                      x
                                     Arom
Za
                                      ●
                                      x
                                       
                                       
                                       
                                      T50
Z5
                                      ●
                                      ●
                                      x
                                       
                                       
                                      T90
Z9
                                      ●
                                      ●
                                      ●
                                      x
                                       
                                       
[1] Indicates "Full minus 1," etc.
[2] Indicates model with intercept only, no fuel parameters.

Fitting history for Bag-2 Formaldehyde  -  with "FM2" selected as best fit model.
                                Fit Parameters

                             Test with respect to
                                     Full

                             Test with respect to
                                Previous Model
Model
p
-2lnL
BIC[1]

                                                                        Dev.[1]
                                                                              d
                                                                    Pr>χ[2]
                                                                               
                                                                           Dev.
                                                                              d
                                                                    Pr>χ[2]
Full
5
70.37
81.64

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
FM1
4
70.47
80.12

                                                                        0.09329
                                                                              1
                                                                           0.76
                                                                               
                                                                               
                                                                               
                                                                               
FM2
3
70.61
78.66

                                                                         0.2340
                                                                              2
                                                                           0.87
                                                                               
                                                                         0.1467
                                                                              1
                                                                           0.70
FM3
2
73.29
79.73

                                                                          2.922
                                                                              3
                                                                           0.40
                                                                               
                                                                          2.682
                                                                              1
                                                                           0.10
Null model
1
76.19
81.02

                                                                          5.821
                                                                              4
                                                                           0.21
                                                                               
                                                                          2.900
                                                                              1
                                                                           0.09
[1] A lower value indicates a better fit.

[1] The deviation is the difference in
the -2loglik statistics for the 
nested and reference models,
respectively, per Equation 14.

 Coefficients and Type-III Tests of Effect for the Full and Best-Fit Models  -  Formaldehyde (Bag 2).
Effect
                                       
                                  Full Model

                             Best-Fit Model (FM2)

Estimate
Std.Err.
d.f.
t-value
Pr>t

Estimate
Std.Err.
d.f.
t-value
Pr>t
Intercept
                                                                               
                                                                        -8.6574
                                                                         0.1372
                                                                           5.01
                                                                         -63.10
                                                                    <0.00001

                                                                        -8.6574
                                                                         0.1375
                                                                           5.01
                                                                         -62.97
                                                                    <0.00001
Ze
                                                                               
                                                                        0.08456
                                                                        0.05937
                                                                          58.04
                                                                          1.424
                                                                           0.16

                                                                        0.07804
                                                                        0.05011
                                                                          58.08
                                                                           1.56
                                                                          0.125
Za
                                                                               
                                                                        0.01575
                                                                        0.05154
                                                                          58.05
                                                                          0.306
                                                                           0.76

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
Z5
                                                                               
                                                                        0.01863
                                                                        0.05815
                                                                          58.03
                                                                          0.320
                                                                           0.75

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
Z9
                                                                               
                                                                       -0.08138
                                                                        0.05031
                                                                          58.16
                                                                          -1.62
                                                                           0.11

                                                                       -0.08322
                                                                        -0.8322
                                                                          58.15
                                                                          -1.65
                                                                          0.103

                                                                               
                                                                        0.08205
                                                                               
                                                                               
                                                                               
                                                                               

                                                                        0.08239
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                         0.3762
                                                                               
                                                                               
                                                                               
                                                                               

                                                                         0.3776