regression models for ordinal responses a review of methods

Substituting equation 10 in the polytomous logistic

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Unformatted text preview: e polytomous logistic model7,8 is a straight forward extension of the logistic model for binary responses, to accommodate multinomial responses. Unlike the models discussed above, the polytomous logistic model does not impose any restrictions on the ordinality of the response. The model has the following representation: where øj may be thought of as ‘scores’ assigned to the response yj.12 Note that since βk = 0, we have øk = 0, and a further constraint, ø1 = 1 (in order to uniquely identify the parameters when using estimated scores12). Substituting equation (10) in the polytomous logistic model (8) yields the stereotype model: Pr(Y = yjx) = exp (αj + x′βj) Σ k l=1 , 6. Stereotype Logistic Model The most flexible model for analysing an ordinal response is the polytomous logistic model, where β represents the log odds ratio for (Y = yj) versus (Y = y0) per unit change in xl. The polytomous logistic model, however, fails to utilize the ordering of the response categories of Y. Anderson10 proposed modelling the regression coefficients, βj, by imposing the (linear) relati...
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