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Unformatted text preview: with analysis examples using a
data set from a perinatal health programme. We then
describe briefly the statistical software that were used
to fit these models. Finally, the paper concludes with a
discussion on the choice of ordinal model. REGRESSION MODELS FOR
1. Cumulative Logit Model
Attempts to extend the logistic regression model for
binary responses to allow for ordinal responses have
often involved modelling cumulative logits. Consider a
multinominal response variable Y with categorical outcomes, denoted by 1,2,…, k , and let x i denote a
p-dimensional vector of covariates. When no confusion
arises, the subscript ‘i’ will be dropped. The cumulative
logit model was originally proposed by Walker and ‘fair’ versus ‘good’), and ( ‘good’ versus ‘very good’). Duncan3 and later called the proportional odds model
by McCullagh.4 The dependence of Y on x for the proportional odds model has the following representation: Pr(Y yjx) = exp (αj – x′β)
1 + exp (αj – x′β ) , j = 1,2,…,k (1) or equivalently can be re-expressed in logit form as Πj log it(Πj ) = log 1 – Πj Pr (Y yjx) l...
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This document was uploaded on 02/25/2014.
- Spring '11