Unformatted text preview: mption of proportionality 1325 REGRESSION MODELS FOR ORDINAL RESPONSES in the logodds 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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 Spring '11

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