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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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 Spring '11

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