Two-Part Predictors in Regression Models

Researchers often build regression models to relate a response to a set of predictor variables. In some cases, there are predictors that apply to some participants, or to some measurement occasions, but not others. For example, a romantic partner's substance use may be a key predictor of one's own substance use. However, not all participants have a partner, and in a longitudinal study, participants may have a partner during only some occasions. This could be viewed as missing data, but of a very distinctive type: the values are not just unknown but also undefined. In this paper, we present a simple method to accommodate this situation, along with a motivating example, the algebraic justification, a simulation study, and examples on how to carry out the technique.