Modeling Nonnegative Data with Clumping at Zero: A Survey

Applications in which data take nonnegative values but have a substantial proportion of values at zero occur in many disciplines. The modeling of such “clumped-at-zero” or “zero-inflated” data is challenging. We survey models that have been proposed. We consider cases in which the response for the non-zero observations is continuous and in which it is discrete. For the continuous and then the discrete case, we review models for analyzing cross-sectional data. We then summarize extensions for repeated measurement analyses (e.g., in longitudinal studies), for which the literature is still sparse. We also mention applications in which more than one clump can occur and we suggest problems for future research.