regression models for ordinal responses a review of methods

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Unformatted text preview: sus ‘above fair’ (Y 2). These data are suggestive of a trend in the log-odds ratios. Fitting a proportional odds model (model 2) to the above data resulted in a log-odds ratio (se) of 1326 INTERNATIONAL JOURNAL OF EPIDEMIOLOGY TABLE 2 Results of fitting partial proportional odds models: Analgesic trial dataa ˆ β ± se (β ) ˆˆ a 2.3 12.0 31.1 37.0 19.1 0.2 0.1248 0.0005 0.0001 0.0001 0.0001 0.7114 0.7013 ± 0.4491 0.8463 ± 0.3552 0.9272 ± 0.5891 Constrained model Drug Constraint Drug (2 d.f.) Likelihood ratio test (2 d.f.) Goodness-of-fit : linear constraint–drug Test for proportional odds Unconstrained model Drug Response good Response v. good Likelihood ratio test (3 d.f.) Test for nonproportional odds (2 d.f.) Drug (3 d.f.) χ2 0.6899 ± 0.4495 0.9216 ± 0.2661 Variable 2.4 6.4 10.7 37.2 11.8 30.3 0.1184 0.0116 0.0011 0.0001 0.0028 0.0001 P-value Source: ref.2 Data illustrated in Table 1. 1.7710 (0.3625), with the assumption of the proportionality of odds being violated (P 0.001). Hence, fit of a proportion...
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