### Example 18.7 Likelihood Ratio Test

This example is an extension of Example 18.6; it performs another specification test, the likelihood ratio test (LR). Suppose you are interested in testing whether the nested logit model (Output 18.5.1) with three subgroups that represent commuters who arrive early, on time, and late is more appropriate than the standard multinomial logit. This can be done by adding the TEST statement to the model as follows:

```/*-- Restricted Model with Inclusive Value Parameters
Constrained to One --*/
proc mdc data=small maxit=200 outest=a;
model decision = r15 r10 ttime ttime_cp sde sde_cp
sdl sdlx d2l /
type=nlogit
choice=(alt);
id id;
utility u(1, ) = r15 r10 ttime ttime_cp sde sde_cp
sdl sdlx d2l;
nest level(1) = (1 2 3 4 5 6 7 8 @ 1, 9 @ 2, 10 11 12 @ 3),
level(2) = (1 2 3 @ 1);
test INC_L2G1C1=1, INC_L2G1C2=1, INC_L2G1C3=1 /LR;
run;
```

Output 18.7.1: Likelihood Ratio Test

The MDC Procedure

Nested Logit Estimates

Test Results
Test Type Statistic Pr > ChiSq Label
Test0 L.R. 8.11 0.0438 INC_L2G1C1 = 1 , INC_L2G1C2 = 1 , INC_L2G1C3 = 1

Based on this test, you can conclude that the inclusive values, `INC_L2G1C1`, `INC_L2G1C2`, and `INC_L2G1C3` are jointly statistically different from the value 1 at the 5% level and therefore the nested logit is a more appropriate model. The LR test can be used to test other types of restrictions in the nested logit setting as long as one model can be nested within another.