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.1f
                              Final Model Fitting
                       Total Hydrocarbons (THC) (Bag 3)


No. Observations:			956
No. Vehicles:		  		  15    
No. censored measurements:		    2
No. missing measurements:		    0
No. measurements removed:		    0
Model Type:				Mixed model








I.1f.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). 

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). 














THC (Bag 3):  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 included in models ranked 1-9 comprise the "superset" for final model-fitting).


      Models fit for THC (Bag 3): (all models include an intercept term).
Model Term
                                   Notation
                                     Model

                                       
                                   Superset
                                    SM2[1]
                                      SM4
                                       
                                    SM5[2]
                                     etOH
Ze
                                      ●
                                      ●
                                      ●
                                       
                                      x
                                     Arom
Za
                                      ●
                                      ●
                                      ●
                                       
                                      ●
                                      RVP
Zr
                                      ●
                                      ●
                                      x
                                       
                                      ●
                                      T50
Z5
                                      ●
                                      ●
                                      ●
                                       
                                      ●
                                      T90
Z9
                                      ●
                                      ●
                                      ●
                                       
                                      ●
                                 etOH x etOH
ZZee
                                      ●
                                      x
                                       
                                       
                                       
                                  T50 x T50
ZZ55
                                      ●
                                      x
                                       
                                       
                                       
                                 etOH x Arom
ZZea
                                      ---
                                      ---
                                      ---
                                       
                                      ---
                                  etOH x RVP
ZZer
                                      ●
                                      ●
                                      x
                                       
                                      x
                                  etOH x T50
ZZe5
                                      ●
                                      ●
                                      ●
                                       
                                      x
                                  etOH x T90
ZZe9
                                      ---
                                      ---
                                      ---
                                       
                                      ---
                                       

                                       
                                       
                                       
                                       
                                       
[1] Represents "Superset minus 2," etc.
[2] Not nested within SM4; test with respect to SM2.

 THC (Bag 3): Model fitting history, starting with the 10-term superset model.
                                Fit Parameters

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

                                                                           Dev.
                                                                              d
                                                                    Pr>χ[2]
Superset
                                                                             10
527.403
559.900

                                                                               
                                                                               
                                                                               
SM2[2]
                                                                              8
530.138
557.218

                                                                          2.735
                                                                              2
                                                                          0.255
SM4
                                                                              6
556.555
534.890

                                                                          4.753
                                                                              2
                                                                         0.0929

                                                                               



                                                                               
                                                                               
                                                                               
SM5
                                                                              5
562.345
543.388

                                                                         13.250
                                                                              3
                                                                        0.00413

                                                                               



                                                                               
                                                                               
                                                                               
[1] A lower value indicates a better fit.
[2] Best fit with respect to the 11-term design model.
[3] Not nested within SM4; test with respect to SM2.












THC (Bag 3): Coefficients and Tests of Effect for the Superset and Reduced Models, with respect to the 11-term design model. 











I.1f.2	Model Fitting with respect to the 16-term extended Model.
Extended 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 Criterion (BIC) vs. number of terms in model (p) for subset of models respecting hierarchy (CLOSEUP of previous figure).

 Extended Model (16-terms):  Bayesian Information Criterion (BIC) vs. number of terms in model (p) for subset of models respecting hierarchy (CLOSEUP of previous figure).















THC (Bag 3):  Number of terms (p), Goodness-of-fit (BIC) and terms included in the 35 best-fitting candidate models (out of a total of 2,964 possible models with hierarchy).  (Terms included in models ranked 1-9 comprise the "superset" for final model-fitting).
 


NOTE:  Model fitting for 16-term extended model has results identical to that for the 11-term design model, as presented above.

