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Ordered Regression Models
book

Ordered Regression Models

by Andrew S. Fullerton, Jun Xu
April 2016
Intermediate to advanced content levelIntermediate to advanced
188 pages
7h 28m
English
Chapman and Hall/CRC
Content preview from Ordered Regression Models
51Parallel Models
ηη
()
()
−−
=
−≤
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 coefcients. 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
()()
()
−≤−− =
−≤
loglog
1Pr|
1Pr1|
ym
ym
m
x
x
xηη
()
()
−≤
−≤
loglog 1Pr| log1 Pr 1|ym ym
m
xx
xηη
()
{}{}
() ()
−−
−− −≤
(2.30)
If we use λ
m
{x} to represent log{1Pr (ym
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Publisher Resources

ISBN: 9781466569744