  Studies of alcohol and drug use are often interested in the number of days
that people use the substance of interest over an interval, such as 28 days
before a survey date. Although count models are often used for this purpose,
they are not strictly appropriate for this type of data because the response
variable is bounded above. Furthermore, if some peoples' substance use
behaviors are characterized by various weekly patterns of use, summaries of
substance days-of-use used over longer periods can exhibit multiple modes.
These characteristics of substance days-of-use data are not easily fitted with
conventional parametric model families. We propose a continuation ratio ordinal
model for substance days-of-use data. Instead of grouping the set of possible
response values into a small set of ordinal categories, each possible value is
assigned its own category. This allows the exact numeric distribution implied
by the predicted ordinal response to be recovered. We demonstrate the proposed
model using survey data reporting days of alcohol use over 28-day intervals. We
show the continuation ratio model is better able to capture the complexity in
the drinking days dataset compared to binomial, hurdle-negative binomial and
beta-binomial models.
