Unformatted text preview: al odds model to the data is inappropriate, and may result in incorrect or misleading
inferences.
3a. Unconstrained partialproportional odds model.
The partialproportional odds model model6 permits
nonproportional odds for a subset q of the ppredictors
(q p). In addition, the assumption of proportional
odds can be tested for the subset q. With Y being
an ordinal variable with k categories, and x being a
pdimensional vector of covariates, the model suggested for the cumulative probabilities is Pr(Y yjx) = exp (–αj – x′β – t′γj)
1 + exp (–αj – x′β – t′γj) versus yj 1. However, estimation of odds ratios associated with the remaining cumulative probabilities
involve incrementing (α + x′β) by t′γj.
3b. Constrained partialproportional odds model .
Peterson and Harrell,6 in addition to the partialproportional odds model, propose another model called
the ‘constrained partialproportional odds model’. In
the analgesic trial example (Table 1), we noted the
existence of a linear relationship in the logodds ratios
between the drugs and the response. Although fitting
model (6) to the data in Table 1 will require two γjl
parameters, a model constraining the γjl to account for
the linearity (in logodds ratios) in j would require an
additional parameter in the m...
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 Spring '11
 Regression Analysis, Logit, proportional odds, Ordinal Model

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