Unformatted text preview: gh γ is not dependent on j, it is
multiplied by the fixed scalar constant j in the computation of the jth cumulative logit.
Results of fitting the unconstrained (model 6) and constrained partialproportional odds (model 7) models to
the analgesic trial data (Table 1) are contrasted in Table 2.
It was demonstrated earlier that the data did not satisfy
the proportional odds assumption, and that a monotonically
increasing trend in the logodds ratios was observed in the
different logits. Hence, a constrained (partialproportional 1327 REGRESSION MODELS FOR ORDINAL RESPONSES odds) model was fit, with the specification of the following constraints: 1 = 0, 2 = 1, and 3 = 2.
The logodds ratio when the response is dichoˆ
tomized at (yj = 1) is β (0.6899), while the logodds
ratios associated with the second and third cumulative
ˆ
ˆ
ˆ
ˆ
logits are β + ˆ2γ (0.6899 + 0.9216) and β + ˆ3γ
(0.6899 + 2 * 0.9216), respectively. A simultaneous two
degrees of freedom test of H0 : β = 0, γ = 0, was rejected (χ2 =...
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 Spring '11
 Regression Analysis, Logit, proportional odds, Ordinal Model

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