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

Many-levelled continuation ratio models for frequency of alcohol and drug use data