Document ID: EPA-HQ-OAR-2011-0135-0662
Agency: epa
Document Type: Supporting & Related Material
Title: 
Posted Date: 2013-04-18T04:00Z

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  K.3
                                       
                                       
                         Model Fitting Information for
                             Acetaldehyde (Bag 2)

This appendix summarizes model fitting for Bag-2 acetaldehyde.  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 Acetaldehyde
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 no terms except an intercept.

Fitting history for Bag-2 Acetaldehyde  -  with "FM3" 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
71.62
82.89

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
FM1
4
71.87
81.53

                                                                           1.66
                                                                              2
                                                                           0.43
                                                                               
                                                                           0.25
                                                                              1
                                                                           0.62
FM2
3
73.92
81.96

                                                                           3.71
                                                                              3
                                                                           0.29
                                                                               
                                                                           2.04
                                                                              1
                                                                           0.15
FM3
2
76.44
82.87

                                                                           6.23
                                                                              4
                                                                           0.18
                                                                               
                                                                           2.52
                                                                              1
                                                                           0.11
Null model
1
88.03
92.86

                                                                          17.82
                                                                              5
                                                                         0.0032
                                                                               
                                                                          11.59
                                                                              1
                                                                        0.00066
[1] A lower value indicates a better fit.

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

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

                             Best-Fit Model (MM3)

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

Estimate
Std.Err.
d.f.
t-value
Pr>t
Intercept
                                                                               
                                                                        -9.4189
                                                                         0.1177
                                                                              5
                                                                          -80.1
                                                                       0.000000

                                                                        -9.4192
                                                                         0.1162
                                                                          5.007
                                                                          -81.1
                                                                       0.000000
Ze
                                                                               
                                                                         0.1520
                                                                        0.06080
                                                                             58
                                                                           2.50
                                                                         0.0152

                                                                         0.1910
                                                                        0.05306
                                                                          58.13
                                                                           3.60
                                                                        0.00066
Za
                                                                               
                                                                        0.07991
                                                                        0.05279
                                                                             58
                                                                           1.51
                                                                          0.136

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
Z5
                                                                               
                                                                       -0.02997
                                                                        0.05957
                                                                             58
                                                                         -0.503
                                                                          0.617

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
Z9
                                                                               
                                                                       -0.07836
                                                                        0.05153
                                                                             58
                                                                          -1.52
                                                                          0.134

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                        0.05654
                                                                               
                                                                               
                                                                               
                                                                               

                                                                        0.05372
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                         0.3814
                                                                               
                                                                               
                                                                               
                                                                               

                                                                         0.4153