Multinomial logit models are used to model relationships between a polytomous response variable and
a set of regressor variables. These polytomous response models can be classified into two distinct types,
depending on whether the response variable has an ordered or unordered structure.
In an ordered model, the response Y of an individual unit is restricted to one of m ordered values. For
example, the severity of a medical condition may be: none, mild, and severe. The cumulative logit
model assumes that the ordinal nature of the observed response is due to methodological limitations
in collecting the data that results in lumping together values of an otherwise continuous response
variable (McKelvey and Zavoina 1975). Suppose Y takes values y1, y2, . . . , ym on some scale, where
y1 < y2 < . . . < ym. It is assumed that the observable variable is a categorized version of a continuous
latent variable U such that
Y = yi , i−1 < U i, i = 1,
Introduction