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Unformatted text preview: = exp {–βl(xl(1) – xl(0))} (3) 2. ContinuationRatio Model
Feinberg 5 proposed an alternative method (to the
proportional odds model) for the analysis of categorical
data with ordered responses. When the cumulative
probabilities, ∏ j = Pr ( Y y j), of being in one of
the first j categories in the cumulative logit model
(model 2) is replaced by the probability of being in
category j [i.e. θj = Pr(Y = yj)] conditional on being
in categories greater than j [i.e. (1 – ∏j)], this results in
the continuationratio model. Define δj = θj /(1 – ∏j).
The continuationratio model can then be formulated as:
δ
log it (δj ) = log j
1 – δ j Pr (Y = yjx) log = αj – x ′ β , j = 1, 2,…, k Pr (Y yjx) (4) and could essentially be viewed as the ratio of the two conditional probabilities, Pr(Y = yjx) and Pr(Y yjx).
This model of conditional odds has been referred to as
the ‘continuationratio’ model.5 When the ‘logit’ link is
replaced by the ‘complimentary log–log’ link function
in model (4), the resulting model is
log [– log (δj)] =...
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This document was uploaded on 02/25/2014.
 Spring '11

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