Zero-inflated Multivariate Tobit Regression Modeling

A frequent challenge encountered in real-world applications is data having a high proportion of zeros. Focusing on ecological abundance data, much attention has been given to zero-inflated count data. Models for non-negative continuous abundance data with an excess of zeros are rarely discussed. Work presented here considers the creation of a point mass at zero through a left-censoring approach or through a hurdle approach. We incorporate both mechanisms to capture the analogue of zero-inflation for count data. Additionally, primary attention has been given to univariate zero-inflated modeling (e.g., single species), whereas data often arise jointly (e.g., a collection of species). With multivariate abundance data, a key issue is to capture dependence among the species at a site, both in terms of positive abundance as well as absence. Therefore, our contribution is a model for multivariate zero-inflated continuous data that are non-negative. Working in a Bayesian framework, we discuss the issue of separating the two sources of zeros and offer model comparison metrics for multivariate zero-inflated data. In an application, we model the total biomass for five tree species obtained from plots established in the Forest Inventory Analysis database in the Northeast region of the United States.