
114 Ordered Regression Models
necessary partial model for the LR test: β
11
= β
21
and β
11
= β
31
. In this partial model, the parallel
regression assumption is retained for x
1
but relaxed for the remaining variables. The degrees
of freedom for the Wald or LR test for x
1
is 2 because there are two constraints. We can test the
parallel regression assumption for each variable separately by applying similar constraints
and by estimating the appropriate partial models for the LR tests. For each LR test, the non-
parallel model is the unconstrained model, and the partial model is the constrained model.
However, there is no reason that the nonparallel ord ...