ABSTRACT
In this chapter, we discuss those categorical logistic models that are not examined in the previous two chapters, but which are not panel models. The conditional logit model can be used as the foundation of several categorical response choice models, such as McFadden’s alternative-specifi c choice model and rank-ordered logistic regression. All three models are constructed as panel models, where a case may consist of more than one line in the data. For example, a patient may be tested four times, with each testing incidence being represented as a single observation. The lines associated with a case may be identifi ed by a variable, such as id, group, or case. For example:
The models we discuss in this chapter continue to be case specifi c, that is, one line per observation. They were developed to address specifi c problems that the more traditional models failed to accommodate. Few commercial software applications support the models we address in this chapter. Those that do as of 2008 are identifi ed below, along with the section of the chapter in which they are discussed. 12.2 Continuation ratio (Stata, SAS, LogXact) 12.3 Stereotype logistic regression (Stata, SAS) 12.4 Heterogeneous choice logistic model (Stata, user authored)
12.5 Adjacent category logistic model (SAS, LogXact, Limdep) 12.6 Binomial ordered models (Stata, SAS, SPSS, Limdep, others)
The continuation ratio model may be formulated using the following relationship (Feinberg 1980):
ln[Pr(Y = yj|x)/Pr(Y > yj|x)] = α j – xβ(12.1)
where
j = 1, 2, 3,…,J
or
ln[Pr(Y = yj |x)] – ln[Pr(Y > yj |x)] (12.2)
In many ordered logistic regression modeling situations, the response levels are such that the lowest level must occur before the second, the second before the third, and so forth until the highest level. There is even more information lost in such a relationship, if modeled using multinomial methods-or even standard-ordered logistic levels. The Continuation Ratio model incorporates this type of priority into its algorithm. We can model the relationship of education level to religiosity, controlling for having children, age, and gender using the edreligion data set. We will use Stata’s ocratio command to model the data. Moreover, we can assess if priority does make a difference by checking the respective model AIC goodness-of-fi t statistics.
