regression models for ordinal responses a review of methods

The proportional odds model is invariant when the

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Unformatted text preview: mption of proportionality 1325 REGRESSION MODELS FOR ORDINAL RESPONSES in the log-odds ratio (β), and may formally be stated as a test of the null hypothesis H0 : β1 = β2 = ,…, = βk. The proportional odds model is invariant when the codes for the response Y are reversed4,12 (i.e. y1 recoded as yk, y2 recoded as yk–1, and so on), resulting only in a reversal of the sign of the regression parameters. Secondly, the proportional odds model is invariant under collapsability of the categories of the ordinal response.11 This property implies that when the categories of Y are deleted or collapsed, the coefficients β will remain unchanged, although the intercept parameters α will be affected. The collapsibility property of the proportional odds model enables one to model an ordinal outcome Y which may be continuous. Greenland12 provides a more detailed review of these properties. Based on the fit of model (2), the cumulative odds ratio, Ψl , for the lth binary covariate, xl , can be obtained by the following relationship: ΨP = Pr(Y yjxl(1)) Pr(Y yjxl(0))...
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