I'm reading Tuerlinkx & Wang, "Models for Polytomous Data". They write: "Apart from the intercept, the predictors that are included in the predictor matrix X can be classified into seven groups: item predictors, person predictors, logit predictors, and the four combinations of them. ... A logit predictor has the same value in all rows of the predictor matrix referring to the same component of the vector-valued link function. Interactions between a logit predictor and any of the other predictors are also possible."
I don't understand what a logit predictor is. If it has the same value in all rows, then it sounds like it's just the intercept term. But from the first sentence it sounds like there's also another intercept term? And how can you have an interaction between an intercept and another predictor?
It'd be helpful to see a model matrix, but table 3.1 doesn't answer my questions.