
41Parallel Models
Therefore, the effect of x
k
on the log odds of 1 versus 2 is β
k1
− β
k2
and the effect of
x
k
on the log odds of 2 versus 3 is β
k2
− β
k3
. Using this example, the parallel adjacent
category logit model is equivalent to a multinomial logit model with the following
constraints:
Constraint #1: β
k2
− β
k3
= β
k3
or β
k2
= 2β
k3
Constraint #2: β
k1
− 2β
k3
= β
k3
or β
k1
= 3β
k3
With the application of these constraints and a slightly different parameterization of the
model, τ
m
– x𝛃 rather than τ
m
+ x𝛃, the multinomial logit model becomes equivalent to the
parallel adjacent category logit model.
We also consider the probit version of the model ...