regression models for ordinal responses a review of methods

A more detailed discussion can be found in mccullagh

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Unformatted text preview: j – x′β (5) which is the Cox proportional-hazards model13 for survival data in discrete time.13–15 Läära and Mathews16 explicitly prove that when the complimentary log-log link is used, the proportional odds and the continuationratio models are identical. A more detailed discussion can be found in McCullagh 4 and McCullagh and Nelder.14 The odds ratio’s, ΨC, based on continuation-ratios for the lth covariate x1 can be obtained directly from model (4) as follows: ΨC = Pr(Y = yjxl(1))/Pr(Y yjxl(1) ) Pr(Y = yjxl(0))/Pr(Y yjxl(0) ) = exp {–βl(xl(1) – xl(0))} The continuation-ratio model is best suited to circumstances where the individual categories of the response variable are of intrinsic interest, and are not merely an arbitrary grouping of an underlying continuous variable.14 Unlike the proportional odds model (model 2), the continuation-ratio model (model 4) is neither preserved by a reversal of the codes for the ordinal response nor under collapsibility of the categories of Y.12 3. Partial-Proportional Odds Model The primary motivation for the development of the...
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