regression models for ordinal responses a review of methods

# With y being an ordinal variable with k categories

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Unformatted text preview: al odds model to the data is inappropriate, and may result in incorrect or misleading inferences. 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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