regression models for ordinal responses a review of methods

7013 07013 08463 and 07013 09272 for the three

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Unformatted text preview: 31.1, 2 d.f.). However, since the goodnessof-fit of the linearity constraint6 was not satisfied (χ2 = 19.9, 1 d.f., P 0.0001), the model was rejected in favour of the unconstrained model. The fit of the unconstrained model implies that no constraints are placed in the estimation of the log-odds ratios. Hence, instead of using one constrained parameter in the model (as in model 6), 2 – γj parameters associated with the response are used for the second and third cumulative logits. The estimated log-odds ratios are 0.7013, 0.7013 + 0.8463 and 0.7013 + 0.9272 for the three cumulative logits, respectively. where αk = 0 and βk = 0. The parameter β1 corresponds to the regression coefficient for the log-odds of (Y = y1) relative to (Y = y2); β2 corresponds to the log-odds of (Y = y2) relative to (Y = y3), and so on, and there are (k – 1) intercept parameters αj. Exponentiating the regression coefficient βl, for the lth covariate xl will result in the odds ratio comparing (Y = yj) versus (Y = yj+1), for a unit increase in xl. 4. Polytomous Logistic Model Th...
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