Unformatted text preview: al odds model to the data is inappropriate, and may result in incorrect or misleading
3a. Unconstrained partial-proportional odds model.
The partial-proportional odds model model6 permits
non-proportional odds for a subset q of the p-predictors
(q p). In addition, the assumption of proportional
odds can be tested for the sub-set q. With Y being
an ordinal variable with k categories, and x being a
p-dimensional 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 partial-proportional odds model .
Peterson and Harrell,6 in addition to the partialproportional odds model, propose another model called
the ‘constrained partial-proportional odds model’. In
the analgesic trial example (Table 1), we noted the
existence of a linear relationship in the log-odds 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 log-odds ratios) in j would require an
additional parameter in the m...
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- Spring '11
- Regression Analysis, Logit, proportional odds, Ordinal Model