On the effects of structural zeros in regression models

Count variables are commonly used in public health research. However, the count variables often do not precisely capture differences among subjects in a study population of interest. For example, drinking outcomes such as the number of days of any alcohol drinking (DAD) over a period of time are often used to assess alcohol use in alcohol studies. A DAD value of 0 for a subject could mean that the subject was continually abstinent from drinking such as lifetime abstainers or that the subject was alcoholic, but happened not to use any alcohol during the period of time considered. In statistical analysis, zeros of the first kind are referred to as structural zeros, to distinguish them from the second type, sampling zeros. As the example indicates, the structural and sampling zeros represent two groups of subjects with quite different psychosocial outcomes. Although many recent studies have begun to explicitly account for the differences between the two types of zeros in modeling drinking variables as responses, none have acknowledged the implications of the different types of zeros when such drinking variables are used as predictors. This chapter is an updated version of He et al. (J Data Sci 12(3), 2014), where we first attempted to tackle the issue and illustrate the importance of disentangling the structural and sampling zeros in alcohol research using simulated as well as real study data.