Estimating Causal Effects with Zero-Inflated Outcomes

Background Outcomes with excessive zeros commonly occur in randomized experiments across many fields in social science. For example, we might estimate the consequence of periodic surveys on students’ participation activity during a massive online open course (MOOC). If we use the number of posts in online discussions as a measure of engagement, the majority of students who initially sign up for the MOOC will not partake in any online discussions and hence have zero engagement. But the distribution of engagement levels for those who do participate is right-skewed with a very long tail [1]. This is further complicated by introducing randomized experiments targeted at increasing engagement. A treatment effect might show itself in several ways: a smaller proportion of disengaged students, an overall increase in mean engagement, or an increase in mean engagement amongst those who showed any sign of engagement. Various statistical models have been developed to handle count data with excess zeros, the two basic ones being the zero-inflated Poisson model and the hurdle model. Although extensive progress has been made on how to fit these models, the statistics literature provides scarce guidance on how to conduct causal inference for data with excess zeros. Typically, papers presenting results from a zero-inflated or hurdle regression analysis show separate treatment effect estimates for the susceptible probability (corresponding to the structural zeros model) and the susceptible population mean (corresponding to the count model). While the causal estimands are relatively straightforward for some models, eg the hurdle …