Unformatted text preview: 31.1, 2 d.f.). However, since the goodnessoffit 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 logodds
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 logodds 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 logodds of (Y = y1)
relative to (Y = y2); β2 corresponds to the logodds 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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This document was uploaded on 02/25/2014.
 Spring '11

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