Another general model for ordered categorical data is the adjacent categories model. As before, we let p_{ij} be the probability that individual i falls into category j of the dependent variable, and we assume that the categories are ordered in the sequence j=1, ..., J. Now take any pair of categories that are adjacent, such as j and j+1. We can write a logit model for the contrast between these two categories as a function of explanatory variables:

Equation 6.5

where β_{j}x_{i} = β_{ji}x_{il} +...+ β_{jk}x_{ik}. There are J–1 of these paired contrasts. It turns out that this is just another way of writing the multinomial logit ...

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