
51Parallel Models
ηη
()
−−
=
−≤−
=θ −
x
x
x
ym
ym
m
Parallelcontinuationratio:log log1
Pr |
1Pr1|
(2.29)
where τ and θ are the cutpoints, x is the vector of independent variables, and β and η
are vectors of coefcients. Based on Laara and Matthews (1985, p. 206), we can rewrite
Equation 2.29 in order to show that β = η. First, we can express Equation 2.29 in terms of
cumulative probabilities:
loglog
1Pr1|Pr|
1Pr1|
ym ym
ym
m
xx
x
xηη
()
−
−≤−− =
−≤−
=θ −
loglog
1Pr|
1Pr1|
ym
ym
m
x
x
xηη
()
−
−≤
−≤−
=θ −
loglog 1Pr| log1 Pr 1|ym ym
m
xηη
−−≤
−− −≤−
=θ − (2.30)
If we use λ
m
{x} to represent −log{1−Pr (y ≤ m