A more general model can be specified using the nested logit model.
Consider, for example, the following random utility function:

Suppose the set of all alternatives indexed by is partitioned into nests, . The nested logit model is obtained by assuming that the error term in the utility function has the GEV cumulative distribution function

where is a measure of a degree of independence among the alternatives in nest . When for all , the model reduces to the standard logit model.
Since the public transportation modes, 1 and 2, tend to be correlated, these two choices can be grouped together. The decision tree displayed in Figure 18.8 is constructed.
Figure 18.8: Decision Tree for Model Choice
The twolevel decision tree is specified in the NEST statement. The NCHOICE= option is not allowed for nested logit estimation. Instead, the CHOICE= option needs to be specified, as in the following statements:
/* nested logit estimation */ proc mdc data=newdata; model decision = ttime / type=nlogit choice=(mode 1 2 3) covest=hess; id pid; utility u(1,) = ttime; nest level(1) = (1 2 @ 1, 3 @ 2), level(2) = (1 2 @ 1); run;
In Figure 18.9, estimates of the inclusive value parameters, INC_L2G1C1
and INC_L2G1C2
, are indicative of a nested model structure. See the section Nested Logit and the section Decision Tree and Nested Logit for more details about inclusive values.
Figure 18.9: TwoLevel Nested Logit Estimates
Parameter Estimates  

Parameter  DF  Estimate  Standard Error 
t Value  Approx Pr > t 
ttime_L1  1  0.4040  0.1241  3.25  0.0011 
INC_L2G1C1  1  0.8016  0.4352  1.84  0.0655 
INC_L2G1C2  1  0.8087  0.3591  2.25  0.0243 
The nested logit model is estimated with the restriction INC_L2G1C1
= INC_L2G1C2
by specifying the SAMESCALE option, as in the following statements:
/* nlogit with samescale option */ proc mdc data=newdata; model decision = ttime / type=nlogit choice=(mode 1 2 3) samescale covest=hess; id pid; utility u(1,) = ttime; nest level(1) = (1 2 @ 1, 3 @ 2), level(2) = (1 2 @ 1); run;
The estimation result is displayed in Figure 18.10.
Figure 18.10: Nested Logit Estimates with One Dissimilarity Parameter
Parameter Estimates  

Parameter  DF  Estimate  Standard Error 
t Value  Approx Pr > t 
ttime_L1  1  0.4025  0.1217  3.31  0.0009 
INC_L2G1  1  0.8209  0.3019  2.72  0.0066 
The nested logit model is equivalent to the conditional logit model if INC_L2G1C1
= INC_L2G1C2
= . You can verify this relationship by estimating a constrained nested logit model as shown in the following statements. (See
the section RESTRICT Statement for details about imposing linear restrictions on parameter estimates.)
/* constrained nested logit estimation */ proc mdc data=newdata; model decision = ttime / type=nlogit choice=(mode 1 2 3) covest=hess; id pid; utility u(1,) = ttime; nest level(1) = (1 2 @ 1, 3 @ 2), level(2) = (1 2 @ 1); restrict INC_L2G1C1 = 1, INC_L2G1C2 =1; run;
The parameter estimates and the active linear constraints for the constrained nested logit model are displayed in Figure 18.11.
Figure 18.11: Constrained Nested Logit Estimates
Parameter Estimates  

Parameter  DF  Estimate  Standard Error 
t Value  Approx Pr > t 
Parameter Label 
ttime_L1  1  0.3572  0.0776  4.60  <.0001  
INC_L2G1C1  0  1.0000  0  
INC_L2G1C2  0  1.0000  0  
Restrict1  1  2.1706  8.4098  0.26  0.7993*  Linear EC [ 1 ] 
Restrict2  1  3.6573  10.0001  0.37  0.7186*  Linear EC [ 2 ] 
Linearly Independent Active Linear Constraints  

1  0  =  1.0000  +  1.0000  *  INC_L2G1C1 
2  0  =  1.0000  +  1.0000  *  INC_L2G1C2 