regression models for ordinal responses a review of methods

We then describe briefly the statistical software

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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 ORDINAL RESPONSES 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.

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